Highest Common Factor of 406, 961, 415 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 406, 961, 415 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 406, 961, 415 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 406, 961, 415 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 406, 961, 415 is 1.

HCF(406, 961, 415) = 1

HCF of 406, 961, 415 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 406, 961, 415 is 1.

Highest Common Factor of 406,961,415 using Euclid's algorithm

Highest Common Factor of 406,961,415 is 1

Step 1: Since 961 > 406, we apply the division lemma to 961 and 406, to get

961 = 406 x 2 + 149

Step 2: Since the reminder 406 ≠ 0, we apply division lemma to 149 and 406, to get

406 = 149 x 2 + 108

Step 3: We consider the new divisor 149 and the new remainder 108, and apply the division lemma to get

149 = 108 x 1 + 41

We consider the new divisor 108 and the new remainder 41,and apply the division lemma to get

108 = 41 x 2 + 26

We consider the new divisor 41 and the new remainder 26,and apply the division lemma to get

41 = 26 x 1 + 15

We consider the new divisor 26 and the new remainder 15,and apply the division lemma to get

26 = 15 x 1 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 406 and 961 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(26,15) = HCF(41,26) = HCF(108,41) = HCF(149,108) = HCF(406,149) = HCF(961,406) .

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

Step 1: Since 415 > 1, we apply the division lemma to 415 and 1, to get

415 = 1 x 415 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 415 is 1

Notice that 1 = HCF(415,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 406, 961, 415 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 406, 961, 415?

Answer: HCF of 406, 961, 415 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 406, 961, 415 using Euclid's Algorithm?

Answer: For arbitrary numbers 406, 961, 415 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.