Highest Common Factor of 498, 310, 222, 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, 310, 222, 635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 498, 310, 222, 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, 310, 222, 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, 310, 222, 635 is 1.

HCF(498, 310, 222, 635) = 1

HCF of 498, 310, 222, 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, 310, 222, 635 is 1.

Highest Common Factor of 498,310,222,635 using Euclid's algorithm

Highest Common Factor of 498,310,222,635 is 1

Step 1: Since 498 > 310, we apply the division lemma to 498 and 310, to get

498 = 310 x 1 + 188

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 188 and 310, to get

310 = 188 x 1 + 122

Step 3: We consider the new divisor 188 and the new remainder 122, and apply the division lemma to get

188 = 122 x 1 + 66

We consider the new divisor 122 and the new remainder 66,and apply the division lemma to get

122 = 66 x 1 + 56

We consider the new divisor 66 and the new remainder 56,and apply the division lemma to get

66 = 56 x 1 + 10

We consider the new divisor 56 and the new remainder 10,and apply the division lemma to get

56 = 10 x 5 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 498 and 310 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(56,10) = HCF(66,56) = HCF(122,66) = HCF(188,122) = HCF(310,188) = HCF(498,310) .

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

Step 1: Since 222 > 2, we apply the division lemma to 222 and 2, to get

222 = 2 x 111 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 222 is 2

Notice that 2 = HCF(222,2) .

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

Step 1: Since 635 > 2, we apply the division lemma to 635 and 2, to get

635 = 2 x 317 + 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 635 is 1

Notice that 1 = HCF(2,1) = HCF(635,2) .

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Frequently Asked Questions on HCF of 498, 310, 222, 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, 310, 222, 635?

Answer: HCF of 498, 310, 222, 635 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 498, 310, 222, 635 using Euclid's Algorithm?

Answer: For arbitrary numbers 498, 310, 222, 635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.