Factors Questions with Solutions | Set 1 (Q1 to Q10)

This set contains Factors Questions with Solutions — Set 1 (Q1 to Q10) covering number of factors, sum of factors, product of factors and prime factorization — from basic to advanced — exactly as asked in real competitive exams.

Solutions are written in a simple, step-by-step notebook style for easy self-study and quick understanding. Each solution is broken down step by step so even the toughest question feels easy. These questions are hand-picked for students preparing for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. International students preparing for GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests will find these equally useful.

✏️ Attempt each question on your own first — then check the solution below.

1. Find the number of factors of 500.

2. Find the number of even factors of 800.

3. Find the number of odd factors of 800.

4. Find the number of factors, odd factors and even factors of 1240.

5. Find the total number fo factors, odd factors and even factors of 2⁵ × 3² × 5³ × 7² × 11

6. Find the number of factors of 2⁵ × 3² × 5³ × 7² × 11 that are divisible by 10, divisible by 100, divisible by 1000.

7. Given a number
           2⁵×3²×5³×7²×11
(i) Find the sum of all factors
(ii) Find the sum of even factors
(iii) Find the sum of odd factors.

8. Find the number of prime factors of:
6⁶ × 8⁸ × 10¹⁰ × 12¹² × 14¹⁴

9. Given a number:
1480
(i) Find number of all factors
(ii) Find the number of even factors
(iii) Find number of odd factors
(iv) Find number of prime factors
(v) Sum of all factors
(vi) Sum of even factors
(vii) Sum of odd factors

10. Find the number of factors of 24³ – 16³ – 8³

1. Find the number of factors of 500.
Sol:
500 = 5 × 10 × 10 = 2² × 5³
∴ Number of factors = (2 + 1)(3 + 1) = 12      Answer

2. Find the number of even factors of 800.
Sol:
800 = 8 × 10 × 10 = 8 × 2 × 5 × 2 × 5 = 2⁵ × 5²

3. Find the number of odd factors of 800.
Sol:
800 = 2⁵ × 5²

4. Find the number of factors, odd factors and even factors of 1240.
Sol:
1240 = 124 × 10 = 31 × 4 × 10 = 2³ × 5 × 31
total number of factors ⟹ (3 + 1)(1 + 1)(1 + 1) = 16     Answer

5. Find the total number fo factors, odd factors and even factors of 2⁵ × 3² × 5³ × 7² × 11
Sol:
Total number of factors = (5 + 1)(2 + 1)(3 + 1)(2 + 1)(1 + 1)
 = 432       Answer

= 5 × (2 + 1)(3 + 1)(2 + 1)(1 + 1)
 = 360         Answer

Number of odd factors ⟹ 3² × 5³ × 7² × 11¹
= (2 + 1)(3 + 1)(2 + 1)(1 + 1)
 = 72    Answer

6. Find the number of factors of 2⁵ × 3² × 5³ × 7² × 11 that are divisible by 10, divisible by 100, divisible by 1000.
Sol:
Factors that are divisible by 10 ⟹

= 5 × (2 + 1) × 3 × (2 + 1) × (1 + 1)
= 270      Answer

Factors that are divisible by 100 ⟹ 

= 4 × (2 + 1) × 2 × (2 + 1) × (1 + 1)
= 144     Answer

Factors that are divisible by 1000 ⟹ 
1000 = 2³ × 5³

= 3 × (2 + 1) × 1 × (2 + 1) × (1 + 1)
= 54    Answer

7. Given a number
           2⁵×3²×5³×7²×11

(i) Find the sum of all factors
(ii) Find the sum of even factors
(iii) Find the sum of odd factors.
Sol:-
(i) Sum of all factors ⟹
(2⁰ + 2¹ + 2² + 2³ +2⁴ +2⁵)(3⁰ + 3¹ + 3²)(5⁰ + 5¹ + 5² + 5³)(7⁰ + 7¹ + 7²)(11⁰ + 11¹)
=(63)(13)(156)(57)(12)
= 87390576               Answer

8. Find the number of prime factors of:
           6⁶×8⁸×10¹⁰×12¹²×14¹⁴
Sol:- Given expression can be re-written as:
(2×3)⁶×(2)⁸×(2×5)¹×(2×3)¹²×(2×7)¹⁴
= 2⁷⁸×3¹⁸×5¹⁰×7¹⁴
Just add all powers as it is to get number of prime factors which in this case is:-
78 + 1 8+10 + 14
= 120          Answer

9. Given a number:
1480
(i) Find number of all factors
(ii) Find the number of even factors
(iii) Find number of odd factors
(iv) Find number of prime factors
(v) Sum of all factors
(vi) Sum of even factors
(vii) Sum of odd factors
Sol:-    1480=148×10 = 4×37×10 =2³×5×37

∴ number of all factors = 4×2×2
                                           = 16            Answer

∴ number of even factors = 3×2×2 = 12     Answer

∴ number of odd factors 2×2 = 4       Answer

(iv)            2³×5¹×37¹
∴ Number of prime factors = 3 + 1 + 1 = 5         Answer

(v)          (2⁰ + 2¹ + 2²+ 2³)(5⁰ + 5¹)(37⁰ + 37¹)
= (1 + 2 + 4 + 8)(1 + 5)(1 + 37 )
= 3420    ⟵    Sum of all factors         Answer

(vi)         Sum of even factors =
(2¹ + 2² + 2³)(5⁰ + 5¹)(37⁰+ 37¹)
= (14)(6)(38)
= 3192                 Answer

(vii)       Sum of odd factors
= (5⁰ + 5¹)(37⁰ + 37¹)
= 228               Answer

10. Find the number of factors of 24³ – 16³ – 8³
Sol:
8(3³ – 2³ – 1)
= 8³ × 18
= 8³ × 2 × 3²
 = 11 × 3
 =  33    Answer

✅ Well done on completing Set 1!

Continue practising with Factors Questions 11 to 20 → Set 2 or revisit the Factors Concept Page to strengthen your formulas and tricks before moving ahead.

Consistent practice is the key to mastering factors for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and international exams including GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests. Want to understand the concept better? Read about Factors on Wikipedia before attempting the next set.

This page is part of our complete series of factors questions with solutions for competitive exams — covering every question type from basic to advanced so you can build speed, accuracy and confidence. Practising these questions regularly will also strengthen your core factors concept before your exam day.