Find the smallest possible integer y such that 288y is a multiple of 5616.Thanks!

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Mazda12345

What?

Adwin

288 = 2 x 144

= 2 x 2 x 72

= 2 x 2 x 2 x 36

= 2 x 2 x 2 x 2 x 18

= 2 x 2 x 2 x 2 x 2 x 9

= 2 x 2 x 2 x 2 x 2 x 3 x 3

= 2^{5} x 3^{2}

5,616 = 2 x 2,808

= 2 x 2 x 1,404

= 2 x 2 x 2 x 702

= 2 x 2 x 2 x 2 x 351

= 2 x 2 x 2 x 2 x 3 x 117

= 2 x 2 x 2 x 2 x 3 x 3 x 39

= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 13

= 2^{4} x 3^{3} x 13

In order for 288y to be a multiple of 5,616… the prime factors in the final product must be equal to or more than the multiplier.

∴ we just need one more 2

5,616 x 2 = 11,232

288y = 11,232

y = 11,232 ÷ 288

= **39**

**Check:**

288 x 39 = 11,232

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