Highest Common Factor of 975, 413, 864 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 975, 413, 864 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 975, 413, 864 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 975, 413, 864 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 975, 413, 864 is 1.

HCF(975, 413, 864) = 1

HCF of 975, 413, 864 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 975, 413, 864 is 1.

Highest Common Factor of 975,413,864 using Euclid's algorithm

Highest Common Factor of 975,413,864 is 1

Step 1: Since 975 > 413, we apply the division lemma to 975 and 413, to get

975 = 413 x 2 + 149

Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 149 and 413, to get

413 = 149 x 2 + 115

Step 3: We consider the new divisor 149 and the new remainder 115, and apply the division lemma to get

149 = 115 x 1 + 34

We consider the new divisor 115 and the new remainder 34,and apply the division lemma to get

115 = 34 x 3 + 13

We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get

34 = 13 x 2 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 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 975 and 413 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(115,34) = HCF(149,115) = HCF(413,149) = HCF(975,413) .

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

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

864 = 1 x 864 + 0

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

Notice that 1 = HCF(864,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 975, 413, 864 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 975, 413, 864?

Answer: HCF of 975, 413, 864 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 975, 413, 864 using Euclid's Algorithm?

Answer: For arbitrary numbers 975, 413, 864 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.