Highest Common Factor of 752, 620, 977 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 752, 620, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 752, 620, 977 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 752, 620, 977 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 752, 620, 977 is 1.

HCF(752, 620, 977) = 1

HCF of 752, 620, 977 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 752, 620, 977 is 1.

Highest Common Factor of 752,620,977 using Euclid's algorithm

Highest Common Factor of 752,620,977 is 1

Step 1: Since 752 > 620, we apply the division lemma to 752 and 620, to get

752 = 620 x 1 + 132

Step 2: Since the reminder 620 ≠ 0, we apply division lemma to 132 and 620, to get

620 = 132 x 4 + 92

Step 3: We consider the new divisor 132 and the new remainder 92, and apply the division lemma to get

132 = 92 x 1 + 40

We consider the new divisor 92 and the new remainder 40,and apply the division lemma to get

92 = 40 x 2 + 12

We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get

40 = 12 x 3 + 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 752 and 620 is 4

Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(92,40) = HCF(132,92) = HCF(620,132) = HCF(752,620) .

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

Step 1: Since 977 > 4, we apply the division lemma to 977 and 4, to get

977 = 4 x 244 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 977 is 1

Notice that 1 = HCF(4,1) = HCF(977,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 752, 620, 977 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 752, 620, 977?

Answer: HCF of 752, 620, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 752, 620, 977 using Euclid's Algorithm?

Answer: For arbitrary numbers 752, 620, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.