Highest Common Factor of 706, 981, 664 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 706, 981, 664 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 706, 981, 664 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 706, 981, 664 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 706, 981, 664 is 1.

HCF(706, 981, 664) = 1

HCF of 706, 981, 664 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 706, 981, 664 is 1.

Highest Common Factor of 706,981,664 using Euclid's algorithm

Highest Common Factor of 706,981,664 is 1

Step 1: Since 981 > 706, we apply the division lemma to 981 and 706, to get

981 = 706 x 1 + 275

Step 2: Since the reminder 706 ≠ 0, we apply division lemma to 275 and 706, to get

706 = 275 x 2 + 156

Step 3: We consider the new divisor 275 and the new remainder 156, and apply the division lemma to get

275 = 156 x 1 + 119

We consider the new divisor 156 and the new remainder 119,and apply the division lemma to get

156 = 119 x 1 + 37

We consider the new divisor 119 and the new remainder 37,and apply the division lemma to get

119 = 37 x 3 + 8

We consider the new divisor 37 and the new remainder 8,and apply the division lemma to get

37 = 8 x 4 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 706 and 981 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(37,8) = HCF(119,37) = HCF(156,119) = HCF(275,156) = HCF(706,275) = HCF(981,706) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 664 > 1, we apply the division lemma to 664 and 1, to get

664 = 1 x 664 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 664 is 1

Notice that 1 = HCF(664,1) .

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Frequently Asked Questions on HCF of 706, 981, 664 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 706, 981, 664?

Answer: HCF of 706, 981, 664 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 706, 981, 664 using Euclid's Algorithm?

Answer: For arbitrary numbers 706, 981, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.