Find the HCF of the numbers 2520, 3600, 5880.

Correct option is B

Given:
The numbers are 2520, 3600, and 5880.
Formula Used:
Prime factorization method to find the Highest Common Factor (HCF).
HCF is the product of the lowest powers of common prime factors.
Solution:
First, we find the prime factorization of each given number.
2520 = 252 × 10 = (4 × 9 × 7) × (2 × 5) = $$2^{3} × 3^{2} × 5^{1} × 7^{1}$$​​
3600 = 36 × 100 = (4 × 9) × (25 × 4) = $$2^{4} × 3^{2} × 5^{2}$$​​
5880 = 588 × 10 = (4 × 147) × (2 × 5) = (4 × 3 × 49) × (2 × 5) = $$2^{3} × 3^{1} × 5^{1} × 7^{2}$$​​
The common prime factors among all three numbers are 2, 3, and 5.
Now, we take the lowest power of each common prime factor.
Lowest power of 2 = $$2^{3}$$​​
Lowest power of 3 = $$3^{1}$$​​
Lowest power of 5 = $$5^{1}$$​​
The Highest Common Factor (HCF) is the product of these.
HCF = $$2^{3} × 3^{1} × 5^{1}$$​​
HCF = 8 × 3 × 5 = 120
Final Answer
So the correct answer is (b)