Highest Common Factor of 874, 561, 226 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 874, 561, 226 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 874, 561, 226 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 874, 561, 226 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 874, 561, 226 is 1.

HCF(874, 561, 226) = 1

HCF of 874, 561, 226 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 874, 561, 226 is 1.

Highest Common Factor of 874,561,226 using Euclid's algorithm

Highest Common Factor of 874,561,226 is 1

Step 1: Since 874 > 561, we apply the division lemma to 874 and 561, to get

874 = 561 x 1 + 313

Step 2: Since the reminder 561 ≠ 0, we apply division lemma to 313 and 561, to get

561 = 313 x 1 + 248

Step 3: We consider the new divisor 313 and the new remainder 248, and apply the division lemma to get

313 = 248 x 1 + 65

We consider the new divisor 248 and the new remainder 65,and apply the division lemma to get

248 = 65 x 3 + 53

We consider the new divisor 65 and the new remainder 53,and apply the division lemma to get

65 = 53 x 1 + 12

We consider the new divisor 53 and the new remainder 12,and apply the division lemma to get

53 = 12 x 4 + 5

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 874 and 561 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(65,53) = HCF(248,65) = HCF(313,248) = HCF(561,313) = HCF(874,561) .

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

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

226 = 1 x 226 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 226 is 1

Notice that 1 = HCF(226,1) .

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Frequently Asked Questions on HCF of 874, 561, 226 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 874, 561, 226?

Answer: HCF of 874, 561, 226 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 874, 561, 226 using Euclid's Algorithm?

Answer: For arbitrary numbers 874, 561, 226 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.