Question

By using euclid's algorithm, find the hcf of 120, 224 and 256.

Answer 1

The HCF of 120,224 and 256 is 8

Refer to the attachment

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Answer 2

Answer:

The correct answer for the HCF of the three given numbers is found to be: 8.

Step-by-step explanation:

For applying the Euclid's algorithm to find the HCF of three numbers, we first find out the HCF of the two larger numbers, x and then find the HCF of the third number and the found value of x.

We are given the numbers: 120, 224, 256

So, using the Euclid's algorithm on 224 and 256, we get:

$256=224\times 1+32$

The remainder is not 0, so now dividing 224 by 32, we get:

$224=32\times 7+0$

The remainder comes out to be 0, so, the HCF of 224 and 256 is found to be 32.

Now, using the Euclid's Theorem on the numbers 120 and 32, we get:

$120=32\times 3+24$

The remainder is not 0, so now dividing 32 by 24, we get:

$32=24\times 1+8$

The remainder is not 0, so now dividing 24 by 8, we get:

$24=8\times 3+0$

The remainder comes out to be 0, so, the HCF of 32 and 120 is found to be 8.

Thus, the HCF of the three given numbers by Euclid's theorem is found to be 8.