Highest Common Factor of 684, 498, 257, 198 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 684, 498, 257, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 498, 257, 198 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 684, 498, 257, 198 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 684, 498, 257, 198 is 1.

HCF(684, 498, 257, 198) = 1

HCF of 684, 498, 257, 198 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 684, 498, 257, 198 is 1.

Highest Common Factor of 684,498,257,198 using Euclid's algorithm

Highest Common Factor of 684,498,257,198 is 1

Step 1: Since 684 > 498, we apply the division lemma to 684 and 498, to get

684 = 498 x 1 + 186

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 186 and 498, to get

498 = 186 x 2 + 126

Step 3: We consider the new divisor 186 and the new remainder 126, and apply the division lemma to get

186 = 126 x 1 + 60

We consider the new divisor 126 and the new remainder 60,and apply the division lemma to get

126 = 60 x 2 + 6

We consider the new divisor 60 and the new remainder 6,and apply the division lemma to get

60 = 6 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 684 and 498 is 6

Notice that 6 = HCF(60,6) = HCF(126,60) = HCF(186,126) = HCF(498,186) = HCF(684,498) .

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

Step 1: Since 257 > 6, we apply the division lemma to 257 and 6, to get

257 = 6 x 42 + 5

Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get

6 = 5 x 1 + 1

Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 257 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(257,6) .

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

Step 1: Since 198 > 1, we apply the division lemma to 198 and 1, to get

198 = 1 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1

Notice that 1 = HCF(198,1) .

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Frequently Asked Questions on HCF of 684, 498, 257, 198 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 684, 498, 257, 198?

Answer: HCF of 684, 498, 257, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 498, 257, 198 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 498, 257, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.