What are Factors and Multiples ?
Factors
- The numbers which exactly divides the given number are called the Factors of that number.
- Example :
Factors of the number 12 are
1 × 12,
2 × 6,
3 × 4,
4 × 3,
6 × 2 and
12 ×1
Hence 1, 2, 3, 4, 6 and 12 are the factors of 12.
Hence 1, 2, 3, 4, 6 and 12 are the factors of 12.
Multiples
If we say that 4 and 5 are the factors of 20 then 20 is the multiple of 4 and 5 both.List the multiples of 3
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
and so on ,
Hence multiples of 3 are 3,6,9,12,15,18........
- Multiples are always more than or equal to the given number.
Some facts about Factors and Multiples
- 1 is the only number which is the factor of every number.
- Every number is the factor of itself.
- All the factors of any number are the exact divisor of that number.
- All the factors are less than or equal to the given number.
- There are limited numbers of factors of any given number.
- All the multiples of any number are greater than or equal to the given number.
- There are unlimited multiples of any given numbers.
- Every number is a multiple of itself.
Perfect Number
- If the sum of all the factors of any number is equal to the double of that number then that number is called a Perfect Number.
Perfect Number Factors Sum of all the factors 6 1, 2, 3, 6 12 28 1, 2, 4, 7, 14, 28 56 496 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
Common Factors and Common Multiples
Example: 1What are the common factors of 25 and 55?
Solution:
Factors of 25 are 1, 5.
Factors of 55 are 1, 5, 11.
so Common factors of 25 and 55 are 1 and 5.
Example: 2
Find the common multiples of 3 and 4.
Solution:
Common multiples of 3 and 4 are 0, 12, 24 and so on.