Question

Using Euclid's division algorithm, find H.C.F.of $56,96$ and $404.$

• A. $8$
• B. $16$
• C. $12$
• D. $4$

Answer 1

The correct option is D $4$

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,
$96=56\times 1+40$
Since remainder $40\ne 0.$

So,applying Euclid's division lemma to $56$ and $40$ we have,
$56=40\times 1+16$
Since remainder $16\ne 0$

So,applying Euclid's division lemma to $40$ and $16$ we have,
$40=16\times 2+8$
Since remainder $8\ne 0$

So, applying Euclid's division lemma to $16$ and $8$ we have,
$16=8\times 2+0$
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,
$404=8\times 50+4$
Since remainder $4\ne 0$ So,applying Euclid's division lemma to $8$ and $4$ we have,
$8=4\times 2+0$
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 $4.$