Find Greatest Common Divisor of 12, 24, 42 and 60, using prime factorization.

Answer

The GCD of given numbers is 6.

Explanation

Step 1 : Find prime factorization of each number.

12 = 24 = 42 = 60 = 2 \cdot 2 \cdot 3 2 \cdot 2 \cdot 2 \cdot 3 2 \cdot 3 \cdot 7 2 \cdot 2 \cdot 3 \cdot 5

(view steps on how to factor 12, 24, 42 and 60. )

Step 2 : Put a box around factors that are common for all numbers:

12 = 24 = 42 = 60 = 2 \cdot 2 \cdot 3 2 \cdot 2 \cdot 2 \cdot 3 2 \cdot 3 \cdot 7 2 \cdot 2 \cdot 3 \cdot 5

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 3 = 6

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