Highest Common Factor of 369, 964 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 369, 964 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 369, 964 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 369, 964 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 369, 964 is 1.

HCF(369, 964) = 1

HCF of 369, 964 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 369, 964 is 1.

Highest Common Factor of 369,964 using Euclid's algorithm

Highest Common Factor of 369,964 is 1

Step 1: Since 964 > 369, we apply the division lemma to 964 and 369, to get

964 = 369 x 2 + 226

Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 226 and 369, to get

369 = 226 x 1 + 143

Step 3: We consider the new divisor 226 and the new remainder 143, and apply the division lemma to get

226 = 143 x 1 + 83

We consider the new divisor 143 and the new remainder 83,and apply the division lemma to get

143 = 83 x 1 + 60

We consider the new divisor 83 and the new remainder 60,and apply the division lemma to get

83 = 60 x 1 + 23

We consider the new divisor 60 and the new remainder 23,and apply the division lemma to get

60 = 23 x 2 + 14

We consider the new divisor 23 and the new remainder 14,and apply the division lemma to get

23 = 14 x 1 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 369 and 964 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(23,14) = HCF(60,23) = HCF(83,60) = HCF(143,83) = HCF(226,143) = HCF(369,226) = HCF(964,369) .

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Frequently Asked Questions on HCF of 369, 964 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 369, 964?

Answer: HCF of 369, 964 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 369, 964 using Euclid's Algorithm?

Answer: For arbitrary numbers 369, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.