Highest Common Factor of 498, 763, 64 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, 763, 64 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 498, 763, 64 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, 763, 64 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, 763, 64 is 1.

HCF(498, 763, 64) = 1

HCF of 498, 763, 64 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, 763, 64 is 1.

Highest Common Factor of 498,763,64 using Euclid's algorithm

Highest Common Factor of 498,763,64 is 1

Step 1: Since 763 > 498, we apply the division lemma to 763 and 498, to get

763 = 498 x 1 + 265

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 265 and 498, to get

498 = 265 x 1 + 233

Step 3: We consider the new divisor 265 and the new remainder 233, and apply the division lemma to get

265 = 233 x 1 + 32

We consider the new divisor 233 and the new remainder 32,and apply the division lemma to get

233 = 32 x 7 + 9

We consider the new divisor 32 and the new remainder 9,and apply the division lemma to get

32 = 9 x 3 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 498 and 763 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(233,32) = HCF(265,233) = HCF(498,265) = HCF(763,498) .

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

Step 1: Since 64 > 1, we apply the division lemma to 64 and 1, to get

64 = 1 x 64 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 64 is 1

Notice that 1 = HCF(64,1) .

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Frequently Asked Questions on HCF of 498, 763, 64 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, 763, 64?

Answer: HCF of 498, 763, 64 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 498, 763, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 498, 763, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.