Highest Common Factor of 498, 635 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 498, 635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 498, 635 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 498, 635 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 498, 635 is 1.

HCF(498, 635) = 1

HCF of 498, 635 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 498, 635 is 1.

Highest Common Factor of 498,635 using Euclid's algorithm

Highest Common Factor of 498,635 is 1

Step 1: Since 635 > 498, we apply the division lemma to 635 and 498, to get

635 = 498 x 1 + 137

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 137 and 498, to get

498 = 137 x 3 + 87

Step 3: We consider the new divisor 137 and the new remainder 87, and apply the division lemma to get

137 = 87 x 1 + 50

We consider the new divisor 87 and the new remainder 50,and apply the division lemma to get

87 = 50 x 1 + 37

We consider the new divisor 50 and the new remainder 37,and apply the division lemma to get

50 = 37 x 1 + 13

We consider the new divisor 37 and the new remainder 13,and apply the division lemma to get

37 = 13 x 2 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 1

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 498 and 635 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(37,13) = HCF(50,37) = HCF(87,50) = HCF(137,87) = HCF(498,137) = HCF(635,498) .

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Frequently Asked Questions on HCF of 498, 635 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 498, 635?

Answer: HCF of 498, 635 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 498, 635 using Euclid's Algorithm?

Answer: For arbitrary numbers 498, 635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.