Highest Common Factor of 690, 969, 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 690, 969, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 690, 969, 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 690, 969, 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 690, 969, 31 is 1.

HCF(690, 969, 31) = 1

HCF of 690, 969, 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 690, 969, 31 is 1.

Highest Common Factor of 690,969,31 using Euclid's algorithm

Highest Common Factor of 690,969,31 is 1

Step 1: Since 969 > 690, we apply the division lemma to 969 and 690, to get

969 = 690 x 1 + 279

Step 2: Since the reminder 690 ≠ 0, we apply division lemma to 279 and 690, to get

690 = 279 x 2 + 132

Step 3: We consider the new divisor 279 and the new remainder 132, and apply the division lemma to get

279 = 132 x 2 + 15

We consider the new divisor 132 and the new remainder 15,and apply the division lemma to get

132 = 15 x 8 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 690 and 969 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(132,15) = HCF(279,132) = HCF(690,279) = HCF(969,690) .

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

Step 1: Since 31 > 3, we apply the division lemma to 31 and 3, to get

31 = 3 x 10 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 31 is 1

Notice that 1 = HCF(3,1) = HCF(31,3) .

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Frequently Asked Questions on HCF of 690, 969, 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 690, 969, 31?

Answer: HCF of 690, 969, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 690, 969, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 690, 969, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.