Highest Common Factor of 762, 854, 387 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 762, 854, 387 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 762, 854, 387 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 762, 854, 387 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 762, 854, 387 is 1.

HCF(762, 854, 387) = 1

HCF of 762, 854, 387 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 762, 854, 387 is 1.

Highest Common Factor of 762,854,387 using Euclid's algorithm

Highest Common Factor of 762,854,387 is 1

Step 1: Since 854 > 762, we apply the division lemma to 854 and 762, to get

854 = 762 x 1 + 92

Step 2: Since the reminder 762 ≠ 0, we apply division lemma to 92 and 762, to get

762 = 92 x 8 + 26

Step 3: We consider the new divisor 92 and the new remainder 26, and apply the division lemma to get

92 = 26 x 3 + 14

We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get

26 = 14 x 1 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 762 and 854 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(92,26) = HCF(762,92) = HCF(854,762) .

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

Step 1: Since 387 > 2, we apply the division lemma to 387 and 2, to get

387 = 2 x 193 + 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 387 is 1

Notice that 1 = HCF(2,1) = HCF(387,2) .

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Frequently Asked Questions on HCF of 762, 854, 387 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 762, 854, 387?

Answer: HCF of 762, 854, 387 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 762, 854, 387 using Euclid's Algorithm?

Answer: For arbitrary numbers 762, 854, 387 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.