Question

126dividedby 256in Euclid'smethod​

Answer 1

Answer:

HCF of 126, 256 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 126, 256 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 126, 256 is 2.

HCF(126, 256) = 2

HCF of 126, 256 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of two or more Numbers

HCF of:

126, 256

Highest common factor (HCF) of 126, 256 is 2.

Highest Common Factor of 126,256 using Euclid's algorithm

Step 1: Since 256 > 126, we apply the division lemma to 256 and 126, to get

256 = 126 x 2 + 4

Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 4 and 126, to get

126 = 4 x 31 + 2

Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 126 and 256 is 2

Notice that 2 = HCF(4,2) = HCF(126,4) = HCF(256,126) .