How many Factors & Multiples questions come in CAT Quant?

About 0.8 questions in a 22-question Quant section, worth roughly 2 marks. Factors & Multiples appeared in 12 of the 24 CAT papers from 2017 to 2025, 22 questions in all, which ranks it 17 of 25 Quant chapters.

Are Factors & Multiples questions in CAT MCQ or TITA?

46% of the Factors & Multiples questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Factors & Multiples questions does CAT ask?

CAT keeps returning to 6 question shapes in Factors & Multiples: Exponents, matched prime by prime; A fixed product, so list the pairs; Count the divisors with a property; Divisibility of a whole family; Minimise under divisibility constraints; Counting in a range, or consecutive integers.

Factors & Multiples for CAT: Formulas, Weightage & Question Types

Primes one at a time, counting divisors, and listing factor pairs.

Factors & Multiples formula sheet

Everything CAT needs from Factors & Multiples, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. Throughout, $N = p^a q^b r^c \cdots$ is the prime factorisation.

Counting divisors


Number of divisors	$(a+1)(b+1)(c+1)\cdots$
Sum of divisors	$\dfrac{p^{a+1}-1}{p-1} \times \dfrac{q^{b+1}-1}{q-1} \times \cdots$
Product of divisors	$N^{\,d/2}$ , where $d$ is the number of divisors
Perfect-square divisors	count only the even exponents: $\left(\lfloor\frac{a}{2}\rfloor+1\right)\left(\lfloor\frac{b}{2}\rfloor+1\right)\cdots$
Perfect-cube divisors	the same with multiples of 3

What a divisor count tells you


Exactly 2 divisors	a prime
Exactly 3 divisors	$p^2$
Exactly 4 divisors	$p^3$ or $pq$
Exactly $d$ divisors	every way of writing $d$ as a product gives an exponent pattern
$d$ is odd	exactly when $N$ is a perfect square

Factor pairs


Pairs $(a,b)$ with $ab = N$ and $a \le b$	$\left\lceil \dfrac{d}{2} \right\rceil$
$x^2 - y^2 = N$	factor $N$ as $(x-y)(x+y)$ ; both factors must share parity
$\dfrac{1}{a}+\dfrac{1}{b} = \dfrac{1}{k}$	rearranges to $(a-k)(b-k) = k^2$
Any "product equals a constant"	list the factor pairs, including negative ones when integers are allowed

Divisibility


If $k$ divides $A$ and $B$	$k$ divides every $mA + nB$
Count up to $n$ divisible by $a$	$\left\lfloor \dfrac{n}{a} \right\rfloor$
Divisible by none of $a,b,c$	inclusion–exclusion on the counts
Highest power of a prime $p$ in $n!$	$\left\lfloor\frac{n}{p}\right\rfloor + \left\lfloor\frac{n}{p^2}\right\rfloor + \cdots$

Matching exponents


$m^n = p^a q^b$	$n$ must divide every exponent, so $n \mid \gcd(a,b)$
Smallest $n$ with $A \mid B^n$	take the worst prime: $n = \max\lceil \frac{\text{needed}}{\text{available}} \rceil$
Largest integer dividing a family	test the first two or three members and take their gcd

The 6 Factors & Multiples question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

01
Exponents, matched prime by prime
02
A fixed product, so list the pairs
03
Count the divisors with a property
04
Divisibility of a whole family
05
Minimise under divisibility constraints
06
Counting in a range, or consecutive integers

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Factors & Multiples in CAT: quick answers

How many Factors & Multiples questions come in CAT Quant?: About 0.8 questions in a 22-question Quant section, worth roughly 2 marks. Factors & Multiples appeared in 12 of the 24 CAT papers from 2017 to 2025, 22 questions in all, which ranks it 17 of 25 Quant chapters.
Are Factors & Multiples questions in CAT MCQ or TITA?: 46% of the Factors & Multiples questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Factors & Multiples questions does CAT ask?: CAT keeps returning to 6 question shapes in Factors & Multiples: Exponents, matched prime by prime; A fixed product, so list the pairs; Count the divisors with a property; Divisibility of a whole family; Minimise under divisibility constraints; Counting in a range, or consecutive integers.

Factors & Multiples for CAT: Formulas, Weightage & Question Types

Factors & Multiples formula sheet

The 6 Factors & Multiples question types CAT repeats

Is Factors & Multiples costing you marks?

Factors & Multiples in CAT: quick answers

More Number System for CAT