Find Greatest Common Divisor of 210, 230, 250 and 270, using prime factorization.

Answer

The GCD of given numbers is 10.

Explanation

Step 1 : Find prime factorization of each number.

210 = 230 = 250 = 270 = 2 \cdot 3 \cdot 5 \cdot 7 2 \cdot 5 \cdot 23 2 \cdot 5 \cdot 5 \cdot 5 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

(view steps on how to factor 210, 230, 250 and 270. )

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

210 = 230 = 250 = 270 = 2 \cdot 3 \cdot 5 \cdot 7 2 \cdot 5 \cdot 23 2 \cdot 5 \cdot 5 \cdot 5 2 \cdot 3 \cdot 3 \cdot 3 \cdot 5

Step 3 : Multiply the boxed numbers together:

GC D = 2 \cdot 5 = 10

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