NCERT Class X Chapter 1: Real Numbers Exercise 1.1 Question 1(i)

NCERT Class X Chapter 1: Real Numbers Exercise 1.1 Question 1(i)

Question:

Express 140 as a product of its prime factors.

Given:

The number \(140\).

To Find:

The prime factorization of \(140\).

Formula:

To express a number as a product of its prime factors, divide the number repeatedly by the smallest prime numbers until all the factors are prime.

Solution:

Step 1: Divide 140 by 2, the smallest prime number.

$$ 140 \div 2 = 70 $$

Step 2: Divide 70 by 2 again, since 70 is even.

$$ 70 \div 2 = 35 $$

Step 3: 35 is not divisible by 2 or 3. Next, divide by 5.

$$ 35 \div 5 = 7 $$

Step 4: 7 is a prime number, so the process stops here.

Step 5: Write the prime factorization of 140 using exponents for repeated factors.

$$ 140 = 2 \times 2 \times 5 \times 7 = 2^2 \times 5 \times 7 $$

Result:

The prime factorization of \(140\) is:
$$ 140 = 2^2 \times 5 \times 7 $$

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