What is the HCF of 36, 60, and 48?

What is the HCF of 36, 60, and 48?

Step 1: Find the prime factorization of each number.
Step 2: For 36, divide by 2: 36 ÷ 2 = 18, then 18 ÷ 2 = 9, then 9 ÷ 3 = 3, and finally 3 ÷ 3 = 1. So, 36 = 2^2 * 3^2.
Step 3: For 60, divide by 2: 60 ÷ 2 = 30, then 30 ÷ 2 = 15, then 15 ÷ 3 = 5, and finally 5 ÷ 5 = 1. So, 60 = 2^2 * 3^1 * 5^1.
Step 4: For 48, divide by 2: 48 ÷ 2 = 24, then 24 ÷ 2 = 12, then 12 ÷ 2 = 6, then 6 ÷ 2 = 3, and finally 3 ÷ 3 = 1. So, 48 = 2^4 * 3^1.
Step 5: Write down the prime factorizations: 36 = 2^2 * 3^2, 60 = 2^2 * 3^1 * 5^1, 48 = 2^4 * 3^1.
Step 6: Identify the common prime factors and their lowest powers: For 2, the lowest power is 2^2; for 3, the lowest power is 3^1.
Step 7: Multiply the common prime factors: HCF = 2^2 * 3^1 = 4 * 3 = 12.

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