CAT Quant Special Numbers: Squares, Cubes, Factorials
Recognition beats calculation in CAT Quant. This curated special-numbers reference covers perfect squares to 30 squared, cubes to 12 cubed, factorials to 10 factorial, powers of 2 and 3, and the first 15 primes, with where each type appears and a 2-week memorisation plan.
You are three minutes into the quant section, and a question asks for the number of factors of 3,628,800. You know the shortcut, but first you have to see that this value is 10 factorial. Miss that, and you burn a minute multiplying up from scratch. A small list of special numbers in CAT quant quietly removes this tax. Recognition beats calculation. A short set of memorised values turns a slow computation into an instant read.
Most aspirants treat memorisation as a crutch, something you fall back on when you have not learned the real method. For one specific set of numbers, that instinct costs you marks. The perfect squares up to 900, the cubes up to 1728, the factorials up to 10!, and a couple of power sequences show up again and again across the paper. This guide gives you the full reference as a clean table, tells you where each type appears, and lays out a two-week plan to lock it into memory.
Recognition beats calculation: the case for a list
Working memory is small. George Miller's 1956 paper put its capacity at about seven items, and later work revised that down to roughly four chunks. Every second you spend computing 12 cubed on scratch paper is a second working memory is not spending on the logic of the question. Recognise 1728 as 12 cubed on sight, and you free that space for the reasoning that actually earns the mark.
Chunking is the mechanism behind this. A memorised fact becomes a single retrievable unit instead of a multi-step calculation. It is the same reason a strong chess player reads a board at a glance while a beginner counts pieces one by one. Your special numbers list is that kind of vocabulary for quant, and fluency in it changes how a question feels.
The payoff is measurable. A question that hinges on spotting a perfect square can take 45 to 60 seconds if you factorise from scratch, or two seconds if you know the value already. Save that gap on four or five questions, and you have bought yourself an extra attempt in a section where every mark shifts your percentile. This is one of the cheapest speed gains available in your CAT exam preparation.
What counts as a special number in CAT quant
Not every number is worth memorising. The special numbers CAT quant rewards are the ones that recur across topics and whose recognition unlocks a shortcut. Six families cover almost all of them, and each one maps to a part of the syllabus you already study.
- Perfect squares up to 30 squared, which is 900. These anchor number theory, surds, and quadratic work.
- Perfect cubes up to 12 cubed, which is 1728. These appear in mensuration and in number-property questions.
- Factorials up to 10 factorial, which is 3,628,800. These drive permutations, combinations, and counting-based probability.
- Powers of 2 up to 2 to the 15th, which is 32768. These run through remainder and last-digit questions.
- Powers of 3 up to 3 to the 10th, which is 59049. These show up in cyclicity and base-system problems.
- The first 15 prime numbers, up to 47. These underpin factorisation, HCF, and LCM.
Memorise these six families and you cover the large majority of recognition shortcuts the exam hands you. The point is not to know every number. It is to know the specific values that keep reappearing so you never have to rebuild them under the clock. The next section puts all of them in one table.
Recognition memory is faster and more reliable than free recall, a gap documented across decades of memory research. That is why multiple-choice feels easier than a blank page. For quant, the practical version is direction. You do not want to recite squares from 1 to 30 in order. You want to see 529 in a question and know instantly that it is 23 squared. Drilling that reverse direction, value first and identity second, is what converts a memorised list into exam speed.
The special numbers reference table
Here is the full list in one place. Read down the type column, commit the middle column to memory, and use the right column to see where each family earns its keep. Every value below has been checked, so you can trust the list as your single source.
| Number type | Values to memorise | Where it appears in CAT |
|---|---|---|
| Perfect squares (1 to 30 squared) | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 | Number theory, surds, quadratic roots, Pythagorean triples |
| Perfect cubes (1 to 12 cubed) | 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 | Mensuration and volume, number properties, sum-of-cubes questions |
| Factorials (1! to 10!) | 1, 2, 6, 24, 120, 720, 5,040, 40,320, 362,880, 3,628,800 | Permutations, combinations, counting-based probability |
| Powers of 2 (2^1 to 2^15) | 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768 | Remainders, last-digit and cyclicity, binary, geometric progressions |
| Powers of 3 (3^1 to 3^10) | 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049 | Remainders, cyclicity, base-system and number-representation problems |
| First 15 primes | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 | Factorisation, HCF and LCM, counting factors, divisibility |
Two values sit in more than one family, which is worth noticing. 64 is both 8 squared and 4 cubed and 2 to the 6th. 729 is both 27 squared and 9 cubed and 3 to the 6th. When a number belongs to several families at once, it tends to be exactly the value a question is built around, so give those overlaps extra attention.
Where each number type shows up in CAT
Memorising a list is easier when you know why each row matters. Here is the topic behind each family, so the values attach to real questions rather than floating free.
Factorials in permutations and combinations
Permutation and combination questions are built on factorials. When a problem reduces to 7! over something, seeing 7! as 5040 lets you finish instead of expanding the product by hand. Probability questions that count arrangements lean on the same values, since the sample space is often a factorial. Knowing the factorials to 10! covers the range CAT actually sets, and it pairs well with the pattern work in our CAT quant speed drills.
Perfect squares in number theory
Number theory leans on squares constantly. Spotting that 576 is 24 squared tells you it is a perfect square, which changes how you count its factors and test its divisibility. Surd simplification and quadratic roots move faster too, because you recognise the clean value under the root instead of estimating it. The 30 squares up to 900 are the most reused row in the whole table.
Cubes in mensuration and volume
Mensuration and volume questions use cubes directly. A cube of side 12 has volume 1728, and a problem that gives you that volume expects you to read the side straight back. Questions on perfect cubes and on sums of consecutive cubes also reward instant recall of the first twelve, since the arithmetic is trivial once you recognise the value.
Powers in remainders and last-digit questions
Remainder and last-digit problems revolve around powers of 2 and 3. The last digit of a power repeats in a short cycle, and anchoring that cycle is easier when you already know 2 to the 10th is 1024 or 3 to the 4th is 81. Geometric progressions with a ratio of 2 or 3, and questions on binary or base-3 representation, use the same sequences. The first 15 primes support the divisibility and factor-counting side of the same topic. The same recognition-over-recall logic drives our list of CAT trigonometry formulas, where knowing the standard values on sight saves the same 30 to 60 seconds.
The 2-week memorisation protocol
You do not memorise this list by staring at it. Two findings from memory research do the real work: spacing and self-testing. Hermann Ebbinghaus mapped the forgetting curve in 1885 and showed that review spread across days holds far better than a single long session. The testing effect, studied by Henry Roediger among others, shows that recalling a fact strengthens memory more than re-reading it. The plan below uses both.
Ten focused minutes a day beats an hour of passive reading. The gains are not linear either. The first week feels slow, then the values start arriving before you consciously reach for them, which is exactly the fluency you want on exam day.
Keep a running self-test you can do without the table. Pick ten values at random from across the six families, write what each one is, then check. Score yourself honestly and note which family leaks. Most aspirants find powers of 3 and the higher factorials are the last to stick, so weight your review toward whatever you miss rather than repeating the rows you already own.
Mistakes that waste your memorisation effort
Two failure modes make this work backfire, and both are easy to avoid once you can name them.
The first is one-directional memory. You can recite squares in order, one to thirty, yet freeze when a question shows you 529 and asks what it squares from. The exam always tests the reverse direction, so drill recognition, not recitation. The second is a memorised value you never verified. A single wrong entry, say storing 7! as 5060 instead of 5040, is worse than not knowing it at all, because you will trust it under pressure and never recheck. Verify your list against a calculator once, then rely on it.
A wrong stored value is a close cousin of the avoidable slips covered in our guide to CAT quant silly mistakes, where trusting a shaky number quietly costs marks you should have banked. The other trap is over-memorising. There is no return on learning squares past 900 or factorials past 10!, because CAT does not test them. Stop the list where the syllabus stops, and spend the freed time on the reasoning that these numbers are meant to speed up. For more topic-by-topic quant work, the CAT preparation articles on the blog go deeper on each area.
What to remember
- Recognition is faster than calculation. A short list of special numbers turns a 45 to 60 second computation into a two-second read, which buys extra attempts across the section.
- Six families cover it: squares to 900, cubes to 1728, factorials to 10!, powers of 2 to 32768, powers of 3 to 59049, and the first 15 primes.
- Each family maps to a topic. Factorials to P&C, squares to number theory, cubes to mensuration, powers to remainders and last-digit, primes to factorisation.
- Memorise with spacing and self-testing over two weeks. Squares and cubes first, then factorials and powers, then primes, then timed recognition.
- Drill reverse recognition, not recitation. You need to read 529 and know it is 23 squared, not chant the list in order.
- Verify the list once, then trust it. Do not memorise numbers past the syllabus, and do not carry an unchecked value into the exam.
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