Factors and Divisors
10 lessons · 11 questions · 8 PYQs
What the exams ask here
- number of (proper) divisors of 7200 (JIPMAT 2023 Q12)
- factors of 1800 that are multiples of 6 (Indore 2024 Q1); divisors not divisible by 45 (Indore 2021 Q1)
- perfect-square factors of 3^5 5^8 7^2 (Indore 2025); probability a random factor is a perfect square / a multiple of 10^k (Indore 2020 Q11, 2022 Q38, 2023 Q40)
- sum of (even/odd) divisors; amicable pair of 220 (JIPMAT 2023 Q10)
- product of divisors = N^{d/2}; ways to write N as a product of two factors
- smallest number with exactly k factors; N has 15 factors -> N^2 has ?
- count / sum of integers below N co-prime to N (Euler phi)
Lessons
- Start hereThe idea and the methodFirst lesson of Factors and Divisors
- 1.Count of factors: one formula, two traps2 questions + fresh variantsJIPMAT 20234 min video
- 2.Sum of Factors: One Bracket per Prime1 question + fresh variantsJIPMAT 20235 min video
- 3.Perfect square and cube factors2 questionsIndore 2025 SA6 min video
- 4.Factor Pairs: Count, Don't Double1 question4 min video
- 5.Factors with condition4 questions + fresh variantsIndore 2024 SA
- 6.Product of All Divisors: Pair ThemNew numbers every time (templates)5 min video
- 7.Odd even factorsNotes only
- 8.Smallest number from its factor count1 question + fresh variants5 min video
- 9.Coprimes below nNew numbers every time (templates)