Highest Common Factor of 605, 964 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 605, 964 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 605, 964 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 605, 964 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 605, 964 is 1.

HCF(605, 964) = 1

HCF of 605, 964 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 605, 964 is 1.

Highest Common Factor of 605,964 using Euclid's algorithm

Highest Common Factor of 605,964 is 1

Step 1: Since 964 > 605, we apply the division lemma to 964 and 605, to get

964 = 605 x 1 + 359

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 359 and 605, to get

605 = 359 x 1 + 246

Step 3: We consider the new divisor 359 and the new remainder 246, and apply the division lemma to get

359 = 246 x 1 + 113

We consider the new divisor 246 and the new remainder 113,and apply the division lemma to get

246 = 113 x 2 + 20

We consider the new divisor 113 and the new remainder 20,and apply the division lemma to get

113 = 20 x 5 + 13

We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get

20 = 13 x 1 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 605 and 964 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(113,20) = HCF(246,113) = HCF(359,246) = HCF(605,359) = HCF(964,605) .

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Frequently Asked Questions on HCF of 605, 964 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 605, 964?

Answer: HCF of 605, 964 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 605, 964 using Euclid's Algorithm?

Answer: For arbitrary numbers 605, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.