Highest Common Factor of 772, 410, 832 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 772, 410, 832 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 772, 410, 832 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 772, 410, 832 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 772, 410, 832 is 2.

HCF(772, 410, 832) = 2

HCF of 772, 410, 832 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 772, 410, 832 is 2.

Highest Common Factor of 772,410,832 using Euclid's algorithm

Highest Common Factor of 772,410,832 is 2

Step 1: Since 772 > 410, we apply the division lemma to 772 and 410, to get

772 = 410 x 1 + 362

Step 2: Since the reminder 410 ≠ 0, we apply division lemma to 362 and 410, to get

410 = 362 x 1 + 48

Step 3: We consider the new divisor 362 and the new remainder 48, and apply the division lemma to get

362 = 48 x 7 + 26

We consider the new divisor 48 and the new remainder 26,and apply the division lemma to get

48 = 26 x 1 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

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 772 and 410 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(48,26) = HCF(362,48) = HCF(410,362) = HCF(772,410) .


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

Step 1: Since 832 > 2, we apply the division lemma to 832 and 2, to get

832 = 2 x 416 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 832 is 2

Notice that 2 = HCF(832,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 772, 410, 832 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 772, 410, 832?

Answer: HCF of 772, 410, 832 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 772, 410, 832 using Euclid's Algorithm?

Answer: For arbitrary numbers 772, 410, 832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.