Highest Common Factor of 764, 986, 672 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 764, 986, 672 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 764, 986, 672 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 764, 986, 672 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 764, 986, 672 is 2.

HCF(764, 986, 672) = 2

HCF of 764, 986, 672 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 764, 986, 672 is 2.

Highest Common Factor of 764,986,672 using Euclid's algorithm

Highest Common Factor of 764,986,672 is 2

Step 1: Since 986 > 764, we apply the division lemma to 986 and 764, to get

986 = 764 x 1 + 222

Step 2: Since the reminder 764 ≠ 0, we apply division lemma to 222 and 764, to get

764 = 222 x 3 + 98

Step 3: We consider the new divisor 222 and the new remainder 98, and apply the division lemma to get

222 = 98 x 2 + 26

We consider the new divisor 98 and the new remainder 26,and apply the division lemma to get

98 = 26 x 3 + 20

We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get

26 = 20 x 1 + 6

We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get

20 = 6 x 3 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 764 and 986 is 2

Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(98,26) = HCF(222,98) = HCF(764,222) = HCF(986,764) .

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

Step 1: Since 672 > 2, we apply the division lemma to 672 and 2, to get

672 = 2 x 336 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 672 is 2

Notice that 2 = HCF(672,2) .

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Frequently Asked Questions on HCF of 764, 986, 672 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 764, 986, 672?

Answer: HCF of 764, 986, 672 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 764, 986, 672 using Euclid's Algorithm?

Answer: For arbitrary numbers 764, 986, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.