Factors are numbers that divide a given number exactly without leaving a remainder.
Example: The factors of 12 are 1, 2, 3, 4, 6, and 12
Solved Examples
Example 1: Find all the factors of 64 by the multiplication method.
Solution:
Factors of 64
- 1 × 64 = 64
- 2 × 32 = 64
- 4 × 16 = 64
- 8 × 8 = 64
Hence the factors of 64 are 1, 2, 4, 8, 16, 32, and 64.
Example 2: Find common factors of 24 and 48.
Solution:
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
Hence the common factors of 24 and 48 are 1, 2, 3, 4, 6, 8, 12, and 24.
Example 3: Find all the factors of 32 by the division method.
Solution:
Factors of 32
- 32 ÷ 1 = 32
- 32 ÷ 2 = 16
- 32 ÷ 4 = 8
- 32 ÷ 8 = 4
- 32 ÷ 16 = 2
- 32 ÷ 32 = 1
Hence the factors of 32 are 1, 2, 4, 8, 16, and 32.
Example 4: Check if 50 is a factor of 1550 or not.
Solution:
We have to check the divisibility of 50 and 1550
1550 ÷ 50 = 31 ( with remainder 0)
Hence 1550 is exactly divisible by 50 so 50 is a factor of 1550.
Example 5: Check if 21 is a factor of 525 or not.
Solution:
We will check the divisibility of 525 with 21
On evaluating we get, 525 ÷ 21 = 25, with remainder 0
Here 525 is exactly divisible by 21. Hence 21 is a factor of 525.
Practice Questions
Q1: Find all factors of 28 and 36.
Q2: Check if 12 is a factor of 144 or not.
Q3: Find prime factorization of 169.
Q4: Find prime factorization of 640.
Q5: Find common factors of 12, 24 and 48.