Highest Common Factor of 962, 403, 967 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 962, 403, 967 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 962, 403, 967 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 962, 403, 967 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 962, 403, 967 is 1.

HCF(962, 403, 967) = 1

HCF of 962, 403, 967 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 962, 403, 967 is 1.

Highest Common Factor of 962,403,967 using Euclid's algorithm

Highest Common Factor of 962,403,967 is 1

Step 1: Since 962 > 403, we apply the division lemma to 962 and 403, to get

962 = 403 x 2 + 156

Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 156 and 403, to get

403 = 156 x 2 + 91

Step 3: We consider the new divisor 156 and the new remainder 91, and apply the division lemma to get

156 = 91 x 1 + 65

We consider the new divisor 91 and the new remainder 65,and apply the division lemma to get

91 = 65 x 1 + 26

We consider the new divisor 65 and the new remainder 26,and apply the division lemma to get

65 = 26 x 2 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 962 and 403 is 13

Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(91,65) = HCF(156,91) = HCF(403,156) = HCF(962,403) .

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

Step 1: Since 967 > 13, we apply the division lemma to 967 and 13, to get

967 = 13 x 74 + 5

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 5 and 13, to get

13 = 5 x 2 + 3

Step 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 13 and 967 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(967,13) .

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Frequently Asked Questions on HCF of 962, 403, 967 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 962, 403, 967?

Answer: HCF of 962, 403, 967 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 962, 403, 967 using Euclid's Algorithm?

Answer: For arbitrary numbers 962, 403, 967 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.