NCERT Class X Chapter 1: Real Numbers Exercise 1.1 Question 1(iv)
NCERT Class X Chapter 1: Real Numbers Exercise 1.1 Question 1(iv)
Question:
Express 5005 as a product of its prime factors.
Given:
The number to be factorized is \( 5005 \).
To Find:
Express \( 5005 \) as a product of its prime factors.
Formula:
To write a number as a product of its prime factors, divide it successively by prime numbers starting from the smallest, until the quotient is 1.
Solution:
Step 1: Check divisibility of \( 5005 \) by 2.
\( 5005 \) is odd, so it is not divisible by 2.
Step 2: Check divisibility by 3.
Sum of the digits: \( 5 + 0 + 0 + 5 = 10 \). Since 10 is not divisible by 3, \( 5005 \) is not divisible by 3.
Step 3: Check divisibility by 5.
\( 5005 \) ends in 5, so it is divisible by 5.
$$ 5005 \div 5 = 1001 $$So,
$$ 5005 = 5 \times 1001 $$Step 4: Factorize \( 1001 \).
Check divisibility by 2, 3, and 5. \( 1001 \) is not divisible by any of these.
Now, check divisibility by 7:
$$ 1001 \div 7 = 143 $$So,
$$ 1001 = 7 \times 143 $$Therefore,
$$ 5005 = 5 \times 7 \times 143 $$Step 5: Factorize \( 143 \).
Check divisibility by 2, 3, 5, and 7. \( 143 \) is not divisible by any of these.
Now, check divisibility by 11:
$$ 143 \div 11 = 13 $$So,
$$ 143 = 11 \times 13 $$Therefore,
$$ 5005 = 5 \times 7 \times 11 \times 13 $$Step 6: Check if 13 is a prime number.
13 has only two divisors, 1 and 13, so it is a prime number.
Result:
$$ 5005 = 5 \times 7 \times 11 \times 13 $$
Comments
Post a Comment