Highest Common Factor of 427, 692, 928 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 427, 692, 928 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 427, 692, 928 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 427, 692, 928 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 427, 692, 928 is 1.

HCF(427, 692, 928) = 1

HCF of 427, 692, 928 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 427, 692, 928 is 1.

Highest Common Factor of 427,692,928 using Euclid's algorithm

Highest Common Factor of 427,692,928 is 1

Step 1: Since 692 > 427, we apply the division lemma to 692 and 427, to get

692 = 427 x 1 + 265

Step 2: Since the reminder 427 ≠ 0, we apply division lemma to 265 and 427, to get

427 = 265 x 1 + 162

Step 3: We consider the new divisor 265 and the new remainder 162, and apply the division lemma to get

265 = 162 x 1 + 103

We consider the new divisor 162 and the new remainder 103,and apply the division lemma to get

162 = 103 x 1 + 59

We consider the new divisor 103 and the new remainder 59,and apply the division lemma to get

103 = 59 x 1 + 44

We consider the new divisor 59 and the new remainder 44,and apply the division lemma to get

59 = 44 x 1 + 15

We consider the new divisor 44 and the new remainder 15,and apply the division lemma to get

44 = 15 x 2 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 427 and 692 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(44,15) = HCF(59,44) = HCF(103,59) = HCF(162,103) = HCF(265,162) = HCF(427,265) = HCF(692,427) .

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

Step 1: Since 928 > 1, we apply the division lemma to 928 and 1, to get

928 = 1 x 928 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 928 is 1

Notice that 1 = HCF(928,1) .

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Frequently Asked Questions on HCF of 427, 692, 928 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 427, 692, 928?

Answer: HCF of 427, 692, 928 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 427, 692, 928 using Euclid's Algorithm?

Answer: For arbitrary numbers 427, 692, 928 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.