Highest Common Factor of 972, 628, 840 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 972, 628, 840 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 628, 840 is 4 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 972, 628, 840 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 972, 628, 840 is 4.

HCF(972, 628, 840) = 4

HCF of 972, 628, 840 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 972, 628, 840 is 4.

Highest Common Factor of 972,628,840 using Euclid's algorithm

Highest Common Factor of 972,628,840 is 4

Step 1: Since 972 > 628, we apply the division lemma to 972 and 628, to get

972 = 628 x 1 + 344

Step 2: Since the reminder 628 ≠ 0, we apply division lemma to 344 and 628, to get

628 = 344 x 1 + 284

Step 3: We consider the new divisor 344 and the new remainder 284, and apply the division lemma to get

344 = 284 x 1 + 60

We consider the new divisor 284 and the new remainder 60,and apply the division lemma to get

284 = 60 x 4 + 44

We consider the new divisor 60 and the new remainder 44,and apply the division lemma to get

60 = 44 x 1 + 16

We consider the new divisor 44 and the new remainder 16,and apply the division lemma to get

44 = 16 x 2 + 12

We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get

16 = 12 x 1 + 4

We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get

12 = 4 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 972 and 628 is 4

Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(44,16) = HCF(60,44) = HCF(284,60) = HCF(344,284) = HCF(628,344) = HCF(972,628) .

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

Step 1: Since 840 > 4, we apply the division lemma to 840 and 4, to get

840 = 4 x 210 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 840 is 4

Notice that 4 = HCF(840,4) .

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Frequently Asked Questions on HCF of 972, 628, 840 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 972, 628, 840?

Answer: HCF of 972, 628, 840 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 628, 840 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 628, 840 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.