CAT Number of Factors previous year questions

9 Number of Factors questions from CAT 2022–2025 (Quant), each with its answer and a step-by-step solution.

• Q5In a 3-digit number N , the digits are non-zero and distinct such that none of the digits is a perfect square, and…CAT 2025 Slot 1 · Quant · Number of Factors
• Q11The number of divisors of (2⁶×3⁵×5³×7² ) , which are of the form ( 3r+1 ) , where r is a non-negative integer, isCAT 2025 Slot 2 · Quant · Number of Factors
• Q4Let n be the least positive integer such that 168 is a factor of 1134ⁿ . If m is the least positive integer such that…CAT 2023 Slot 1 · Quant · Number of Factors
• Q1Let a , b , m and n be natural numbers such that a>1 and b>1 . If a^(m)bⁿ=144¹⁴⁵ , then the largest possible value of…CAT 2023 Slot 2 · Quant · Number of Factors
• Q3For any natural numbers m , n , and k , such that k divides both m+2n and 3m+4n , k must be a common divisor ofCAT 2023 Slot 2 · Quant · Number of Factors
• Q6The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, isCAT 2023 Slot 2 · Quant · Number of Factors
• Q2Let n and m be two positive integers such that there are exactly 41 integers greater than 8^(m) and less than 8ⁿ ,…CAT 2023 Slot 3 · Quant · Number of Factors
• Q6The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), isCAT 2023 Slot 3 · Quant · Number of Factors
• Q21Let A be the largest positive integer that divides all the numbers of the form 3^(k)+4^(k)+5^(k) , and B be the…CAT 2022 Slot 1 · Quant · Number of Factors