# IMAT 2019 Q57 [Common factor]

In order to solve this question, we must find the factors of each of the number:

360 = 36 \cdot 10 = 6 \cdot 6 \cdot 5\cdot 2 = 3^2\cdot 2 ^2 \cdot 5\cdot 2 = 2^3 \cdot 3^2 \cdot 5.

500 = 5 \cdot 10^2 = 5 \cdot (5\cdot 2)^2 = 5 \cdot 5^2\cdot 2^2 = 2^2 \cdot 5^3.

700 = 7 \cdot 10^2 = 7\cdot 5^2\cdot 2^2 = 2^2 \cdot 5^2\cdot 7.

From this we can see that all of the numbers have 2^2 \cdot 5 in their prime factors, so the highest common factor is (D) 2^2 \cdot 5

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