Page 44 - Maths Class 06

(h) 1790184
(i) 10000001

3. Is 2430780 divis ible by 7?
4. If a number is divisible by 2 and 7, will it be divisible by 14? Give an example.
5. If a number is divis i ble by 4 and 6, is it neces sary that it will be divis i ble by 24? If not, write one
such number.
6. A number is divis ible by both 5 and 12. By which other number will that number be always
divisible?
7. A number is divis ible by 12. By what other numbers will that number be divisible?

Prime Factorisation

Expressing number as product of its factors is called factorisation. Prime numbers
form the building blocks of any number. Every composite number can be expressed 1
as product of unique primes e g. ., 18 = 2 3 3´ ´ .
Prime factorisation is the method of finding the prime factors of a number that 2 3 5
when multiplied form the given number.

Clearly, the prime factors of 10 are 2 and 5 as 2 ´ 5 yields/gives 10.
For example : Consider, 30 = 2 15´ = 3 10´ = 5 6´

30 30 30 NOTE

2 15 3 10 5 6 Factorisation of a number
means expressing it in
terms of its factors.
3 3 2 5 2 3

In all above factorisations, we ultimately arrive at the same prime factors, i e. . 2 3 5´ ´ and product of 2, 3
and 5 is 30.
This representation of factors is called a factor tree.

We can find the prime factors of any numbers by two methods:
1. Factor tree method 2. Division method

EX AM PLE : Write the prime fac tors of 150 by both the fac tor tree method and di vi sion method.
SO LU TION : Factor Tree Method Long Di vi sion Method
150
2 150

3 × 50 3 75
5 25
3 × 5 × 10
5 5
3 × 5 × 2 × 5
1

\ 150 = 3 5 2 5´ ´ ´ \ 150 = 2 3 5 5´ ´ ´

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