Highest Common Factor of 565, 966, 31 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 565, 966, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 565, 966, 31 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 565, 966, 31 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 565, 966, 31 is 1.

HCF(565, 966, 31) = 1

HCF of 565, 966, 31 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 565, 966, 31 is 1.

Highest Common Factor of 565,966,31 using Euclid's algorithm

Highest Common Factor of 565,966,31 is 1

Step 1: Since 966 > 565, we apply the division lemma to 966 and 565, to get

966 = 565 x 1 + 401

Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 401 and 565, to get

565 = 401 x 1 + 164

Step 3: We consider the new divisor 401 and the new remainder 164, and apply the division lemma to get

401 = 164 x 2 + 73

We consider the new divisor 164 and the new remainder 73,and apply the division lemma to get

164 = 73 x 2 + 18

We consider the new divisor 73 and the new remainder 18,and apply the division lemma to get

73 = 18 x 4 + 1

We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 565 and 966 is 1

Notice that 1 = HCF(18,1) = HCF(73,18) = HCF(164,73) = HCF(401,164) = HCF(565,401) = HCF(966,565) .

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

Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1

Notice that 1 = HCF(31,1) .

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Frequently Asked Questions on HCF of 565, 966, 31 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 565, 966, 31?

Answer: HCF of 565, 966, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 565, 966, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 565, 966, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.