Highest Common Factor of 629, 974 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, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 629, 974 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, 974 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, 974 is 1.

HCF(629, 974) = 1

HCF of 629, 974 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, 974 is 1.

Highest Common Factor of 629,974 using Euclid's algorithm

Highest Common Factor of 629,974 is 1

Step 1: Since 974 > 629, we apply the division lemma to 974 and 629, to get

974 = 629 x 1 + 345

Step 2: Since the reminder 629 ≠ 0, we apply division lemma to 345 and 629, to get

629 = 345 x 1 + 284

Step 3: We consider the new divisor 345 and the new remainder 284, and apply the division lemma to get

345 = 284 x 1 + 61

We consider the new divisor 284 and the new remainder 61,and apply the division lemma to get

284 = 61 x 4 + 40

We consider the new divisor 61 and the new remainder 40,and apply the division lemma to get

61 = 40 x 1 + 21

We consider the new divisor 40 and the new remainder 21,and apply the division lemma to get

40 = 21 x 1 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 629 and 974 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) = HCF(61,40) = HCF(284,61) = HCF(345,284) = HCF(629,345) = HCF(974,629) .

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Frequently Asked Questions on HCF of 629, 974 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, 974?

Answer: HCF of 629, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 629, 974 using Euclid's Algorithm?

Answer: For arbitrary numbers 629, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.