Highest Common Factor of 675, 780, 371 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 675, 780, 371 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 780, 371 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 675, 780, 371 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 675, 780, 371 is 1.

HCF(675, 780, 371) = 1

HCF of 675, 780, 371 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 675, 780, 371 is 1.

Highest Common Factor of 675,780,371 using Euclid's algorithm

Highest Common Factor of 675,780,371 is 1

Step 1: Since 780 > 675, we apply the division lemma to 780 and 675, to get

780 = 675 x 1 + 105

Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 105 and 675, to get

675 = 105 x 6 + 45

Step 3: We consider the new divisor 105 and the new remainder 45, and apply the division lemma to get

105 = 45 x 2 + 15

We consider the new divisor 45 and the new remainder 15, and apply the division lemma to get

45 = 15 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 675 and 780 is 15

Notice that 15 = HCF(45,15) = HCF(105,45) = HCF(675,105) = HCF(780,675) .

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

Step 1: Since 371 > 15, we apply the division lemma to 371 and 15, to get

371 = 15 x 24 + 11

Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 11 and 15, to get

15 = 11 x 1 + 4

Step 3: We consider the new divisor 11 and the new remainder 4, and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

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 15 and 371 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(371,15) .

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Frequently Asked Questions on HCF of 675, 780, 371 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 675, 780, 371?

Answer: HCF of 675, 780, 371 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 780, 371 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 780, 371 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.