Finding number of factors of a number

Concepts Examples

If a number x divides another number y completely then x is a divisor of y. If x is a prime number then x is called the prime factor of number x.

e.g 1,2,3,6 are the factors of 6 and 2,3 are the prime factors of 6.

If any composite number N which can be expressed as N=$a^x\cdot b^y\cdot c^z...$a^x·b^y·c^z... , where a,b,c are the prime numbers and x,y,z are the powers of a,b,c respectively and so on. then the number of factors of N =(x+1)×(y+1)×(z+1)...

e.g Find the number of factors of 24

24=2²×3¹

∴ number of factors of 24 = (3+1)(1+1) = 8

Question 1 Find the total number of factors of 1024 except 1 and 1024 itself.

8	9
10	11

B

1024= 2¹⁰

∴ total number of factors except 1 and 1024 = (10+1) - 2 = 9

Question 2 Find number of factors of 1001

8	3
16	24

A

1001 = 7¹×11¹×13¹

∴ total number of factors = (1+1)(1+1)(1+1) = 2×2×2 = 8

Question 3 Find the total number of factors of 144

15	16
18	25

A

144= 2⁴ × 3²

∴ Number of factors of 144 = (4+1)(2+1) = 15

Question 4 Find the number of factors of 970299

64	32
24	28

D

970299 = 3⁶×11³

∴ total number of factors = (6+1)(3+1) = 7×4 = 28

Question 5 Find the total number of factors of 56 × 324

40	50
60	70

C

56 × 324 = (2³×7¹) × (2²×3⁴)

56 × 324 = 2⁵×3⁴×7¹

∴ total number of factors = (5+1)(4+1)(1+1) = 6 × 5 × 2= 60