Highest Common Factor of 971, 717, 690 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 971, 717, 690 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 971, 717, 690 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 971, 717, 690 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 971, 717, 690 is 1.

HCF(971, 717, 690) = 1

HCF of 971, 717, 690 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 971, 717, 690 is 1.

Highest Common Factor of 971,717,690 using Euclid's algorithm

Highest Common Factor of 971,717,690 is 1

Step 1: Since 971 > 717, we apply the division lemma to 971 and 717, to get

971 = 717 x 1 + 254

Step 2: Since the reminder 717 ≠ 0, we apply division lemma to 254 and 717, to get

717 = 254 x 2 + 209

Step 3: We consider the new divisor 254 and the new remainder 209, and apply the division lemma to get

254 = 209 x 1 + 45

We consider the new divisor 209 and the new remainder 45,and apply the division lemma to get

209 = 45 x 4 + 29

We consider the new divisor 45 and the new remainder 29,and apply the division lemma to get

45 = 29 x 1 + 16

We consider the new divisor 29 and the new remainder 16,and apply the division lemma to get

29 = 16 x 1 + 13

We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get

16 = 13 x 1 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 971 and 717 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(45,29) = HCF(209,45) = HCF(254,209) = HCF(717,254) = HCF(971,717) .

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

Step 1: Since 690 > 1, we apply the division lemma to 690 and 1, to get

690 = 1 x 690 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 690 is 1

Notice that 1 = HCF(690,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 971, 717, 690 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 971, 717, 690?

Answer: HCF of 971, 717, 690 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 971, 717, 690 using Euclid's Algorithm?

Answer: For arbitrary numbers 971, 717, 690 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.