Highest Common Factor of 976, 605, 565 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 976, 605, 565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 976, 605, 565 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 976, 605, 565 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 976, 605, 565 is 1.

HCF(976, 605, 565) = 1

HCF of 976, 605, 565 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 976, 605, 565 is 1.

Highest Common Factor of 976,605,565 using Euclid's algorithm

Highest Common Factor of 976,605,565 is 1

Step 1: Since 976 > 605, we apply the division lemma to 976 and 605, to get

976 = 605 x 1 + 371

Step 2: Since the reminder 605 ≠ 0, we apply division lemma to 371 and 605, to get

605 = 371 x 1 + 234

Step 3: We consider the new divisor 371 and the new remainder 234, and apply the division lemma to get

371 = 234 x 1 + 137

We consider the new divisor 234 and the new remainder 137,and apply the division lemma to get

234 = 137 x 1 + 97

We consider the new divisor 137 and the new remainder 97,and apply the division lemma to get

137 = 97 x 1 + 40

We consider the new divisor 97 and the new remainder 40,and apply the division lemma to get

97 = 40 x 2 + 17

We consider the new divisor 40 and the new remainder 17,and apply the division lemma to get

40 = 17 x 2 + 6

We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get

17 = 6 x 2 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 976 and 605 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(40,17) = HCF(97,40) = HCF(137,97) = HCF(234,137) = HCF(371,234) = HCF(605,371) = HCF(976,605) .

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

Step 1: Since 565 > 1, we apply the division lemma to 565 and 1, to get

565 = 1 x 565 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 565 is 1

Notice that 1 = HCF(565,1) .

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Frequently Asked Questions on HCF of 976, 605, 565 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 976, 605, 565?

Answer: HCF of 976, 605, 565 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 976, 605, 565 using Euclid's Algorithm?

Answer: For arbitrary numbers 976, 605, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.