### Chapter 1: Real Numbers

Q
##### Real Numbers Solutions

Question:

Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Solutions:

(i) 140

We can use the following tree diagram to show the factors of 140.

Hence, the product of prime factors of 140 is 2 x 2 x 5 x 7 = $2^{2}$ x 5 x 7

(ii) 156

We can use the following tree diagram to show the factors of 156.

So, the product of prime factors of 156 is 2 x 2 x 3 x 13 = $2^{2}$ x 3 x 13

(iii) 3825

We can use the following tree diagram to show the factors of 3825.

Hence, the product of prime factors of 3825 is 3 x 3 x 5 x  5 x 17  = $3^{2}$ x $5^{2}$ x 17

(iv) 5005

We can use the following tree diagram to show the factors of 5005.

Hence, the product of prime factors of 5005 is  5 x 7 x 11 x  13.

(v) 7429

We can use the following tree diagram to show the factors of 7429.

Hence, the product of prime factors of 7429 is 17 x 19 x 23 .

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