Find the HCF of the following numbers:

(i) 32, 88
(ii) 108, 288
(iii) 425, 200, 100?

To find the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of a set of numbers, we identify the largest number that divides each of the numbers without leaving a remainder. Let's solve each part step-by-step:
(i) For 32 and 88:

List the factors of each number:

Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88


Identify the common factors: 1, 2, 4, 8

The greatest of these common factors is 8.


Therefore, the HCF of 32 and 88 is 8 .
(ii) For 108 and 288:

Perform the prime factorization of each number:

108 = 2^2 \times 3^3
288 = 2^5 \times 3^2


Find the common prime factors with the lowest exponents:

2^2 (from both)
3^2 (from both)


Multiply these common factors: 2^2 \times 3^2 = 4 \times 9 = 36


Thus, the HCF of 108 and 288 is 36 .
(iii) For 425, 200, and 100:

Perform the prime factorization of each number:

425 = 5^2 \times 17
200 = 2^3 \times 5^2
100 = 2^2 \times 5^2


Identify the common prime factors with the lowest exponents:

5^2 is present in all


The common factor is 5^2 = 25


Therefore, the HCF of 425, 200, and 100 is 25 .
Finding the HCF is useful for simplifying fractions and solving problems involving divisibility. I hope this explanation helps you understand the process better!

Answered by RyanHarmon181 | 2025-07-06