# Ex.1.2 Q1 Real Numbers Solution - NCERT Maths Class 10

## Question

Express each number as a product of its prime factors:

(i) \(140\) (ii) \(156\) (iii) \(3825 \) (iv) \(5005\) (v) \(7429\)

## Text Solution

**What is known?**

A number.

**What is unknown?**

The expression of the given number as a product of its prime factors.

**Reasoning:**

Find the prime factors of the given numbers by prime factorisation method and then multiply the obtained prime numbers to get the product of the prime numbers.

**Steps:**

(i) \(140\)

Prime factors of \(140\)

\[\begin{align}&=2,\;2,\;5,\;7 \\&={{2}^{2}}\times 5\times 7\end{align}\]

(ii) \(156\)

Prime factors of \(156\)

\[\begin{align}&=2\times 2\times 3\times 13 \\ &={{2}^{2}}\times 3\times 13 \end{align}\]

(iii) \(3825\)

Prime factors of \(3825\)

\[\begin{align}&=3\times 3\times 5\times 5\times 17 \\ &={{3}^{2}}\times {{5}^{2}}\times 17\end{align}\]

(iv) \(5005\)

Prime factors of \(5005\)

\[=5\times7\times11\times 13\]

(v) \(7429\)

Prime factors of \(7429\)

\[=17\times 19\times 23\]