Question

Express the following number as a powers of prime factors: (i) 144 (ii) 225

Answer 1

Step-by-step explanation:

1. 144= 12×12

= 3×2×3×2

= 2^2 ×3^2

2. 225 = 15×15

= 3×5×3×5

= 3^2 × 5^2

Answer 2

Given:

Two numbers 144 and 225.

To Find:

To express the given numbers in the powers of prime factors.

Solutions:

1. Prime factorization of a number is defined as expressing the number as the product of prime numbers only.

2. A number is said to be prime if it has only two factors. The two factors are 1 and the number itself.

3. Consider the numbers 144 and 225,

=> Factorizing the first number,

=> 144 = 2 x 72,

=> 144 = 2 x 2 x 36,

=> 144 = 2 x 2 x 2 x 18,

=> 144 = 2 x 2 x 2 x 2 x 9,

=> 144 = 2 x 2 x 2 x 2 x 3 x 3,

=> 144 = (2^4) x (3²)

=> Factorizing the second number,

=> 225 = 3 x 75,

=> 225 = 3 x 3 x 25,

=> 225 = 3 x 3 x 5 x 5,

=> 225 = 3² x 5².

Therefore, the numbers 144 and 225 can be expressed as the powers of prime factors as (2^4) x (3²) and 3² x 5² respectively.