Highest Common Factor of 65, 68, 255, 971 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 65, 68, 255, 971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 65, 68, 255, 971 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 65, 68, 255, 971 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 65, 68, 255, 971 is 1.

HCF(65, 68, 255, 971) = 1

HCF of 65, 68, 255, 971 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 65, 68, 255, 971 is 1.

Highest Common Factor of 65,68,255,971 using Euclid's algorithm

Highest Common Factor of 65,68,255,971 is 1

Step 1: Since 68 > 65, we apply the division lemma to 68 and 65, to get

68 = 65 x 1 + 3

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 3 and 65, to get

65 = 3 x 21 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 65 and 68 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(65,3) = HCF(68,65) .

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

Step 1: Since 255 > 1, we apply the division lemma to 255 and 1, to get

255 = 1 x 255 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 255 is 1

Notice that 1 = HCF(255,1) .

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

Step 1: Since 971 > 1, we apply the division lemma to 971 and 1, to get

971 = 1 x 971 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 971 is 1

Notice that 1 = HCF(971,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 65, 68, 255, 971 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 65, 68, 255, 971?

Answer: HCF of 65, 68, 255, 971 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 65, 68, 255, 971 using Euclid's Algorithm?

Answer: For arbitrary numbers 65, 68, 255, 971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.