If 2520 = 2^a × 3^b × 5^c× 7^d, thena + b – 2c – 3d = _________.

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Solution

Prime factorisation of 2520 is

2520 = 2³ × 3² × 5¹× 7¹

Therefore, a = 3, b = 2, c = 1 and d = 1.

a + b – 2c – 3d = 3 + 2 – 2(1) – 3(1)
= 5 – 2 – 3
= 5 – 5
= 0

Hence, a + b – 2c – 3d = 0.

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