Question

If the HCF of 408 and 1032 is expressible in the form 1032m − 408 × 5, find m.

Answer 1

General integers are 408 and 1032 where 408 < 1032
By applying Euclid’s division lemma, we get
1032 = 408 × 2 + 216
Since remainder ≠ 0, apply division lemma on division 408 and remainder 216
408 = 216 × 1 + 192
Since remainder ≠ 0, apply division lemma on division 216 and remainder 192
216 = 192 × 1 + 24
Since remainder ≠ 0, apply division lemma on division 192 and remainder 24
192 = 24 × 8 + 32
We observe that 32m under in 0. So the last divisor 24 is the H.C.F of 408 and 1032
∴ 216 = 1032m – 408 × 5
⇒ 1032 m = 24 + 408 × 5
⇒ 1032m = 24 + 2040
⇒ 1032m = 2064
⇒ m = 2064/1032 = 2