Page 44 - Math Skill - 5

4 4 F
Factors and Multiplesactors and Multiples

Learning Outcomes

� Factors and Multiples � Divisibility Rules � Lowest Common Multiple (LCM)
� Properties of Factors and Multiples � Prime Factorisation � Properties of LCM and HCF
� Types of Numbers � Highest Common Factor (HCF)

Boot-Up

Mr. Gupta wanted to withdraw ` 5000 from his account in
a bank.
The clerk sitting on the cash counter gave him 50 hundred-
rupee notes.
Did Mr. Gupta get the required amount, i.e., ` 5000?
Of course, he got ` 5000, as 50 hundred-rupee notes
= 50 × ` 100 = ` 5000.

But, if cashier gives notes of denomination other than ` 100,
then can you say that required number of notes are sufficient
to fulfill Mr Gupta’s requirement?

1. ` 200 notes : _______________ 3. ` 20 notes : _______________
2. ` 50 notes : _______________ 4. ` 500 notes : _______________

Factors and Multiples
We have learned that 18 = 1 × 18, 18 = 6 × 3, 18 = 9 × 2.

This shows that each of the numbers, 1, 2, 3, 6, 9 and 18 are factors of 18.
In other words, we can say that 18 is a multiple of each one of the numbers 1, 2, 3, 6, 9 and 18.
Now, let us revise all the properties of factors and multiples.

Properties of Factors and Multiples

S. No. Factors Multiples
1. 1 is a factor of every number. Every number is a multiple of 1.

2. Every number is a factor of itself. Every number is a multiple of itself.
3. Every number is a factor of 0. 0 is a multiple of every number.
4. A factor of a number is less than or equal to Every multiple of a number is greater than or
the number. equal to that number.
5. Every number other than 1 has at least two We can find as many multiples of a number
factors, namely 1 and itself. as we want.