Highest Common Factor of 961, 369 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 961, 369 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 961, 369 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 961, 369 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 961, 369 is 1.

HCF(961, 369) = 1

HCF of 961, 369 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 961, 369 is 1.

Highest Common Factor of 961,369 using Euclid's algorithm

Highest Common Factor of 961,369 is 1

Step 1: Since 961 > 369, we apply the division lemma to 961 and 369, to get

961 = 369 x 2 + 223

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 223 and 369, to get

369 = 223 x 1 + 146

Step 3: We consider the new divisor 223 and the new remainder 146, and apply the division lemma to get

223 = 146 x 1 + 77

We consider the new divisor 146 and the new remainder 77,and apply the division lemma to get

146 = 77 x 1 + 69

We consider the new divisor 77 and the new remainder 69,and apply the division lemma to get

77 = 69 x 1 + 8

We consider the new divisor 69 and the new remainder 8,and apply the division lemma to get

69 = 8 x 8 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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 961 and 369 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(69,8) = HCF(77,69) = HCF(146,77) = HCF(223,146) = HCF(369,223) = HCF(961,369) .

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Frequently Asked Questions on HCF of 961, 369 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 961, 369?

Answer: HCF of 961, 369 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 961, 369 using Euclid's Algorithm?

Answer: For arbitrary numbers 961, 369 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.