Highest Common Factor of 969, 723, 331 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 969, 723, 331 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 969, 723, 331 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 969, 723, 331 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 969, 723, 331 is 1.

HCF(969, 723, 331) = 1

HCF of 969, 723, 331 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 969, 723, 331 is 1.

Highest Common Factor of 969,723,331 using Euclid's algorithm

Highest Common Factor of 969,723,331 is 1

Step 1: Since 969 > 723, we apply the division lemma to 969 and 723, to get

969 = 723 x 1 + 246

Step 2: Since the reminder 723 ≠ 0, we apply division lemma to 246 and 723, to get

723 = 246 x 2 + 231

Step 3: We consider the new divisor 246 and the new remainder 231, and apply the division lemma to get

246 = 231 x 1 + 15

We consider the new divisor 231 and the new remainder 15,and apply the division lemma to get

231 = 15 x 15 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 969 and 723 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(231,15) = HCF(246,231) = HCF(723,246) = HCF(969,723) .

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

Step 1: Since 331 > 3, we apply the division lemma to 331 and 3, to get

331 = 3 x 110 + 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 331 is 1

Notice that 1 = HCF(3,1) = HCF(331,3) .

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Frequently Asked Questions on HCF of 969, 723, 331 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 969, 723, 331?

Answer: HCF of 969, 723, 331 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 969, 723, 331 using Euclid's Algorithm?

Answer: For arbitrary numbers 969, 723, 331 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.