Firstly, the HCF of 408 and 1032 is to be found.
By applying Euclid’s division lemma, we get
1032 = 408 x 2 + 216.
Here, the remainder ≠ 0. So apply Euclid’s division lemma on divisor 408 and remainder 216
408 = 216 x 1 + 192.
As the remainder ≠ 0, again apply division lemma on divisor 216 and remainder 192
216 = 192 x 1 + 24.
Again the remainder ≠ 0. So, apply division lemma again on divisor 192 and remainder 24
192 = 24 x 8 + 0.
Now, it is seen that the remainder is 0.
Hence, the last divisor is the H.C.F of 408 and 1032 i.e., 24
So, this HCF is expressed as a linear combination that is,
24 = 1032 m – 408 x 5
1032 m = 24 + 408 x 5
1032 m = 24 + 2040
1032 m = 2064
m = 2064/1032
∴ m = 2
