Highest Common Factor of 629, 138, 772 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 629, 138, 772 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 629, 138, 772 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 629, 138, 772 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 629, 138, 772 is 1.

HCF(629, 138, 772) = 1

HCF of 629, 138, 772 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 629, 138, 772 is 1.

Highest Common Factor of 629,138,772 using Euclid's algorithm

Highest Common Factor of 629,138,772 is 1

Step 1: Since 629 > 138, we apply the division lemma to 629 and 138, to get

629 = 138 x 4 + 77

Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 77 and 138, to get

138 = 77 x 1 + 61

Step 3: We consider the new divisor 77 and the new remainder 61, and apply the division lemma to get

77 = 61 x 1 + 16

We consider the new divisor 61 and the new remainder 16,and apply the division lemma to get

61 = 16 x 3 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 629 and 138 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(61,16) = HCF(77,61) = HCF(138,77) = HCF(629,138) .

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

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

772 = 1 x 772 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 772 is 1

Notice that 1 = HCF(772,1) .

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Frequently Asked Questions on HCF of 629, 138, 772 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 629, 138, 772?

Answer: HCF of 629, 138, 772 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 629, 138, 772 using Euclid's Algorithm?

Answer: For arbitrary numbers 629, 138, 772 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.