Highest Common Factor of 546, 998, 645 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, 998, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 546, 998, 645 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, 998, 645 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, 998, 645 is 1.

HCF(546, 998, 645) = 1

HCF of 546, 998, 645 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, 998, 645 is 1.

Highest Common Factor of 546,998,645 using Euclid's algorithm

Highest Common Factor of 546,998,645 is 1

Step 1: Since 998 > 546, we apply the division lemma to 998 and 546, to get

998 = 546 x 1 + 452

Step 2: Since the reminder 546 ≠ 0, we apply division lemma to 452 and 546, to get

546 = 452 x 1 + 94

Step 3: We consider the new divisor 452 and the new remainder 94, and apply the division lemma to get

452 = 94 x 4 + 76

We consider the new divisor 94 and the new remainder 76,and apply the division lemma to get

94 = 76 x 1 + 18

We consider the new divisor 76 and the new remainder 18,and apply the division lemma to get

76 = 18 x 4 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 546 and 998 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(76,18) = HCF(94,76) = HCF(452,94) = HCF(546,452) = HCF(998,546) .

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

Step 1: Since 645 > 2, we apply the division lemma to 645 and 2, to get

645 = 2 x 322 + 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 645 is 1

Notice that 1 = HCF(2,1) = HCF(645,2) .

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Frequently Asked Questions on HCF of 546, 998, 645 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, 998, 645?

Answer: HCF of 546, 998, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 546, 998, 645 using Euclid's Algorithm?

Answer: For arbitrary numbers 546, 998, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.