Highest Common Factor of 226, 565, 916 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 226, 565, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 226, 565, 916 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 226, 565, 916 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 226, 565, 916 is 1.

HCF(226, 565, 916) = 1

HCF of 226, 565, 916 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 226, 565, 916 is 1.

Highest Common Factor of 226,565,916 using Euclid's algorithm

Highest Common Factor of 226,565,916 is 1

Step 1: Since 565 > 226, we apply the division lemma to 565 and 226, to get

565 = 226 x 2 + 113

Step 2: Since the reminder 226 ≠ 0, we apply division lemma to 113 and 226, to get

226 = 113 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 113, the HCF of 226 and 565 is 113

Notice that 113 = HCF(226,113) = HCF(565,226) .

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

Step 1: Since 916 > 113, we apply the division lemma to 916 and 113, to get

916 = 113 x 8 + 12

Step 2: Since the reminder 113 ≠ 0, we apply division lemma to 12 and 113, to get

113 = 12 x 9 + 5

Step 3: We consider the new divisor 12 and the new remainder 5, and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 113 and 916 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(113,12) = HCF(916,113) .

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Frequently Asked Questions on HCF of 226, 565, 916 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 226, 565, 916?

Answer: HCF of 226, 565, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 226, 565, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 226, 565, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.