Highest Common Factor of 916, 324, 455 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 916, 324, 455 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 916, 324, 455 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 916, 324, 455 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 916, 324, 455 is 1.

HCF(916, 324, 455) = 1

HCF of 916, 324, 455 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 916, 324, 455 is 1.

Highest Common Factor of 916,324,455 using Euclid's algorithm

Highest Common Factor of 916,324,455 is 1

Step 1: Since 916 > 324, we apply the division lemma to 916 and 324, to get

916 = 324 x 2 + 268

Step 2: Since the reminder 324 ≠ 0, we apply division lemma to 268 and 324, to get

324 = 268 x 1 + 56

Step 3: We consider the new divisor 268 and the new remainder 56, and apply the division lemma to get

268 = 56 x 4 + 44

We consider the new divisor 56 and the new remainder 44,and apply the division lemma to get

56 = 44 x 1 + 12

We consider the new divisor 44 and the new remainder 12,and apply the division lemma to get

44 = 12 x 3 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 916 and 324 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(44,12) = HCF(56,44) = HCF(268,56) = HCF(324,268) = HCF(916,324) .

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

Step 1: Since 455 > 4, we apply the division lemma to 455 and 4, to get

455 = 4 x 113 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 455 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(455,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 916, 324, 455 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 916, 324, 455?

Answer: HCF of 916, 324, 455 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 916, 324, 455 using Euclid's Algorithm?

Answer: For arbitrary numbers 916, 324, 455 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.