Page 19 - NUMINO Challenge_D2

2 Factors

Basic Concepts Finding Factors Using Prime Factorization

The number of factors can be easily found by using prime factorization. After
finding the prime factorization of the given number, write the number of factors
using exponents as shown below. The number of factors is (m 1) (n 1).

18 2 32 Am Bn

Number of factors Number of factors for 32 (2 1)
for 21 (1 1)
1 3 32 Number of factors for 18:
1 1 1 1 3 1 32 (1 1) (2 1) 6

Factors of 18: 1(1 1), 2(2 1),
2 2 1 2 3 2 32

3(1 3), 6(2 3),
9(1 32), 18(2 32)

Example Find all the factors and the number of factors of 72.

Class Notes

The prime factorization of 72 is 72 2 2 .

You can write 72 as 72 23 32 using exponents. If you write the powers of 2 in the row
and the powers of 3 in the column as shown below, you can find all the factors of 72.
Complete the table.

1 2 22 23
1 1 1 1 1 2 2 1 22 4 1 23 8
3 313

32

The factors of 72 starting from the smallest are 1, 2, 3, 4, 6, 8, , , ,
.
, , , and the number of factors is (3 1) (2 1)

Try It Again What is the total number of factors of 36?

16 NUMINO Challenge D2