Highest Common Factor of 640, 312, 922 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 640, 312, 922 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 640, 312, 922 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 640, 312, 922 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 640, 312, 922 is 2.

HCF(640, 312, 922) = 2

HCF of 640, 312, 922 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 640, 312, 922 is 2.

Highest Common Factor of 640,312,922 using Euclid's algorithm

Highest Common Factor of 640,312,922 is 2

Step 1: Since 640 > 312, we apply the division lemma to 640 and 312, to get

640 = 312 x 2 + 16

Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 16 and 312, to get

312 = 16 x 19 + 8

Step 3: We consider the new divisor 16 and the new remainder 8, and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 640 and 312 is 8

Notice that 8 = HCF(16,8) = HCF(312,16) = HCF(640,312) .


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

Step 1: Since 922 > 8, we apply the division lemma to 922 and 8, to get

922 = 8 x 115 + 2

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 922 is 2

Notice that 2 = HCF(8,2) = HCF(922,8) .

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Frequently Asked Questions on HCF of 640, 312, 922 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 640, 312, 922?

Answer: HCF of 640, 312, 922 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 640, 312, 922 using Euclid's Algorithm?

Answer: For arbitrary numbers 640, 312, 922 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.