Find Greatest Common Divisor of 64, 224, 96 and 608, using prime factorization.

Answer

The GCD of given numbers is 32.

Explanation

Step 1 : Find prime factorization of each number.

64 = 224 = 96 = 608 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 7 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 19

(view steps on how to factor 64, 224, 96 and 608. )

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

64 = 224 = 96 = 608 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 7 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 19

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 32

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