Using Euclid's division algorithm, find H.C.F.of 56,96 and 404.
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Let us begin by choosing any two number out of any three number.
Say 56 and 96
As 96 > 56, by applying Euclid's division lemma to 56 and 96 we have,
96 = 56 × 1 + 40
Since remainder 40 ≠ 0.
So,applying Euclid's division lemma to 56 and 40 we have,
56 = 40 × 1 + 16
Since remainder 16 ≠ 0
So,applying Euclid's division lemma to 40 and 16 we have,
40 = 16 × 2 + 8
Since remainder 8 ≠ 0
So, applying Euclid's division lemma to 16 and 8 we have,
16 = 8 × 2 + 0
Since remainder is zero. Hence,divisor 8 is the H.C.F of 56 and 96.
Now,
Again, applying Euclid's division lemma on the H.C.F of the two number and remaining number.
Since, the H.C.F of 56 and 96 is 8 and the remaining number is 404.
So, by applying Euclid's division lemma on 8 and 404 we have,
404 = 8 × 50 + 4
Since remainder 4 ≠0 So,applying Euclid's division lemma to 8 and 4 we have,
8 = 4 × 2 + 0
Hence, remainder is zero.
Hence, remainder 4 is the H.C.F of 8 and 404
Hence, H.C.F. of 404,96 and 56 is 4.