NCERT Class X Chapter 1: Real Numbers Exercise 1.1 Question 1(v)
NCERT Class X Chapter 1: Real Numbers Exercise 1.1 Question 1(v)
Question:
Express 7429 as a product of its prime factors.
Given:
The number given is 7429.
To Find:
Express 7429 as a product of its prime factors.
Formula:
The prime factorization of a number \( n \) is written as:
$$
n = p_1 \times p_2 \times \cdots \times p_k
$$
where each \( p_i \) is a prime number.
Solution:
Step 1: Start dividing 7429 by the smallest prime numbers to find its prime factors.
7429 is not divisible by 2, 3, 5, 7, 11, or 13 (checked by divisibility tests).
Step 2: Check divisibility by 17.
$$ 7429 \div 17 = 437 $$So, 17 is a prime factor. We write:
$$ 7429 = 17 \times 437 $$Step 3: Factorize 437 by dividing by primes.
437 is not divisible by 2, 3, 5, 7, 11, 13, or 17.
Check divisibility by 19:
$$ 437 \div 19 = 23 $$So, 19 is a prime factor. We write:
$$ 437 = 19 \times 23 $$Step 4: 23 is a prime number.
Step 5: Substitute the factors:
$$ 7429 = 17 \times 437 = 17 \times (19 \times 23) = 17 \times 19 \times 23 $$Result:
Prime factorization of 7429:
$$
7429 = 17 \times 19 \times 23
$$
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