Highest Common Factor of 674, 398, 572 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 674, 398, 572 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 674, 398, 572 is 2 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 674, 398, 572 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 674, 398, 572 is 2.

HCF(674, 398, 572) = 2

HCF of 674, 398, 572 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 674, 398, 572 is 2.

Highest Common Factor of 674,398,572 using Euclid's algorithm

Highest Common Factor of 674,398,572 is 2

Step 1: Since 674 > 398, we apply the division lemma to 674 and 398, to get

674 = 398 x 1 + 276

Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 276 and 398, to get

398 = 276 x 1 + 122

Step 3: We consider the new divisor 276 and the new remainder 122, and apply the division lemma to get

276 = 122 x 2 + 32

We consider the new divisor 122 and the new remainder 32,and apply the division lemma to get

122 = 32 x 3 + 26

We consider the new divisor 32 and the new remainder 26,and apply the division lemma to get

32 = 26 x 1 + 6

We consider the new divisor 26 and the new remainder 6,and apply the division lemma to get

26 = 6 x 4 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 674 and 398 is 2

Notice that 2 = HCF(6,2) = HCF(26,6) = HCF(32,26) = HCF(122,32) = HCF(276,122) = HCF(398,276) = HCF(674,398) .

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

Step 1: Since 572 > 2, we apply the division lemma to 572 and 2, to get

572 = 2 x 286 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 572 is 2

Notice that 2 = HCF(572,2) .

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Frequently Asked Questions on HCF of 674, 398, 572 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 674, 398, 572?

Answer: HCF of 674, 398, 572 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 674, 398, 572 using Euclid's Algorithm?

Answer: For arbitrary numbers 674, 398, 572 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.