Highest Common Factor of 674, 870, 381 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, 870, 381 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 674, 870, 381 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 674, 870, 381 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, 870, 381 is 1.

HCF(674, 870, 381) = 1

HCF of 674, 870, 381 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, 870, 381 is 1.

Highest Common Factor of 674,870,381 using Euclid's algorithm

Highest Common Factor of 674,870,381 is 1

Step 1: Since 870 > 674, we apply the division lemma to 870 and 674, to get

870 = 674 x 1 + 196

Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 196 and 674, to get

674 = 196 x 3 + 86

Step 3: We consider the new divisor 196 and the new remainder 86, and apply the division lemma to get

196 = 86 x 2 + 24

We consider the new divisor 86 and the new remainder 24,and apply the division lemma to get

86 = 24 x 3 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 674 and 870 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(86,24) = HCF(196,86) = HCF(674,196) = HCF(870,674) .

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

Step 1: Since 381 > 2, we apply the division lemma to 381 and 2, to get

381 = 2 x 190 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 381 is 1

Notice that 1 = HCF(2,1) = HCF(381,2) .

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Frequently Asked Questions on HCF of 674, 870, 381 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, 870, 381?

Answer: HCF of 674, 870, 381 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 674, 870, 381 using Euclid's Algorithm?

Answer: For arbitrary numbers 674, 870, 381 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.