Highest Common Factor of 546, 915, 854 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, 915, 854 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 546, 915, 854 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, 915, 854 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, 915, 854 is 1.

HCF(546, 915, 854) = 1

HCF of 546, 915, 854 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, 915, 854 is 1.

Highest Common Factor of 546,915,854 using Euclid's algorithm

Highest Common Factor of 546,915,854 is 1

Step 1: Since 915 > 546, we apply the division lemma to 915 and 546, to get

915 = 546 x 1 + 369

Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 369 and 546, to get

546 = 369 x 1 + 177

Step 3: We consider the new divisor 369 and the new remainder 177, and apply the division lemma to get

369 = 177 x 2 + 15

We consider the new divisor 177 and the new remainder 15,and apply the division lemma to get

177 = 15 x 11 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

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

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 546 and 915 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(177,15) = HCF(369,177) = HCF(546,369) = HCF(915,546) .

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

Step 1: Since 854 > 3, we apply the division lemma to 854 and 3, to get

854 = 3 x 284 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 854 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(854,3) .

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Frequently Asked Questions on HCF of 546, 915, 854 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, 915, 854?

Answer: HCF of 546, 915, 854 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 546, 915, 854 using Euclid's Algorithm?

Answer: For arbitrary numbers 546, 915, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.