Highest Common Factor of 891, 706 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 891, 706 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 891, 706 is 1 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 891, 706 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 891, 706 is 1.

HCF(891, 706) = 1

HCF of 891, 706 using Euclid's algorithm

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

HCF of:

Highest common factor (HCF) of 891, 706 is 1.

Highest Common Factor of 891,706 using Euclid's algorithm

Highest Common Factor of 891,706 is 1

Step 1: Since 891 > 706, we apply the division lemma to 891 and 706, to get

891 = 706 x 1 + 185

Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 185 and 706, to get

706 = 185 x 3 + 151

Step 3: We consider the new divisor 185 and the new remainder 151, and apply the division lemma to get

185 = 151 x 1 + 34

We consider the new divisor 151 and the new remainder 34,and apply the division lemma to get

151 = 34 x 4 + 15

We consider the new divisor 34 and the new remainder 15,and apply the division lemma to get

34 = 15 x 2 + 4

We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get

15 = 4 x 3 + 3

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

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 891 and 706 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(34,15) = HCF(151,34) = HCF(185,151) = HCF(706,185) = HCF(891,706) .

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Frequently Asked Questions on HCF of 891, 706 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 891, 706?

Answer: HCF of 891, 706 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 891, 706 using Euclid's Algorithm?

Answer: For arbitrary numbers 891, 706 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.