Highest Common Factor of 546, 715, 428 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 546, 715, 428 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 546, 715, 428 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 546, 715, 428 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 546, 715, 428 is 1.

HCF(546, 715, 428) = 1

HCF of 546, 715, 428 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 546, 715, 428 is 1.

Highest Common Factor of 546,715,428 using Euclid's algorithm

Highest Common Factor of 546,715,428 is 1

Step 1: Since 715 > 546, we apply the division lemma to 715 and 546, to get

715 = 546 x 1 + 169

Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 169 and 546, to get

546 = 169 x 3 + 39

Step 3: We consider the new divisor 169 and the new remainder 39, and apply the division lemma to get

169 = 39 x 4 + 13

We consider the new divisor 39 and the new remainder 13, and apply the division lemma to get

39 = 13 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 546 and 715 is 13

Notice that 13 = HCF(39,13) = HCF(169,39) = HCF(546,169) = HCF(715,546) .

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

Step 1: Since 428 > 13, we apply the division lemma to 428 and 13, to get

428 = 13 x 32 + 12

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 12 and 13, to get

13 = 12 x 1 + 1

Step 3: We consider the new divisor 12 and the new remainder 1, and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 428 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(428,13) .

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Frequently Asked Questions on HCF of 546, 715, 428 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 546, 715, 428?

Answer: HCF of 546, 715, 428 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 546, 715, 428 using Euclid's Algorithm?

Answer: For arbitrary numbers 546, 715, 428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.