Highest Common Factor of 967, 864, 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 967, 864, 964 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 967, 864, 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 967, 864, 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 967, 864, 964 is 1.

HCF(967, 864, 964) = 1

HCF of 967, 864, 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 967, 864, 964 is 1.

Highest Common Factor of 967,864,964 using Euclid's algorithm

Highest Common Factor of 967,864,964 is 1

Step 1: Since 967 > 864, we apply the division lemma to 967 and 864, to get

967 = 864 x 1 + 103

Step 2: Since the reminder 864 ≠ 0, we apply division lemma to 103 and 864, to get

864 = 103 x 8 + 40

Step 3: We consider the new divisor 103 and the new remainder 40, and apply the division lemma to get

103 = 40 x 2 + 23

We consider the new divisor 40 and the new remainder 23,and apply the division lemma to get

40 = 23 x 1 + 17

We consider the new divisor 23 and the new remainder 17,and apply the division lemma to get

23 = 17 x 1 + 6

We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get

17 = 6 x 2 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 967 and 864 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(23,17) = HCF(40,23) = HCF(103,40) = HCF(864,103) = HCF(967,864) .

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

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

964 = 1 x 964 + 0

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

Notice that 1 = HCF(964,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 967, 864, 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 967, 864, 964?

Answer: HCF of 967, 864, 964 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 967, 864, 964 using Euclid's Algorithm?

Answer: For arbitrary numbers 967, 864, 964 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.