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

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

Question:

Express 156 as a product of its prime factors.

Given:

The number 156.

To Find:

The prime factorization of 156.

Formula:

Prime factorization is done by dividing the number by prime numbers successively until all factors are prime.

Solution:

Step 1: Divide 156 by 2 (the smallest prime number) because 156 is even.

$$156 \div 2 = 78$$

Step 2: Divide 78 by 2 again, since 78 is also even.

$$78 \div 2 = 39$$

Step 3: Check 39 for divisibility by 3. The sum of its digits (3 + 9 = 12) is divisible by 3, so divide by 3.

$$39 \div 3 = 13$$

Step 4: 13 is a prime number. Divide 13 by itself.

$$13 \div 13 = 1$$

Step 5: Collect all the prime factors found.

$$156 = 2 \times 2 \times 3 \times 13$$

Step 6: Express repeated factors using exponents.

$$156 = 2^2 \times 3 \times 13$$

Result:

The prime factorization of 156 is:
$$2^2 \times 3 \times 13$$

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