Find Greatest Common Divisor of 36, 54, 90 and 126, using prime factorization.

Answer

The GCD of given numbers is 18.

Explanation

Step 1 : Find prime factorization of each number.

36 = 54 = 90 = 126 = 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 3 \cdot 3 \cdot 3 2 \cdot 3 \cdot 3 \cdot 5 2 \cdot 3 \cdot 3 \cdot 7

(view steps on how to factor 36, 54, 90 and 126. )

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

36 = 54 = 90 = 126 = 2 \cdot 2 \cdot 3 \cdot 3 2 \cdot 3 \cdot 3 \cdot 3 2 \cdot 3 \cdot 3 \cdot 5 2 \cdot 3 \cdot 3 \cdot 7

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 3 \cdot 3 = 18

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