Highest Common Factor of 498, 734, 403 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, 734, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 498, 734, 403 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, 734, 403 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, 734, 403 is 1.

HCF(498, 734, 403) = 1

HCF of 498, 734, 403 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, 734, 403 is 1.

Highest Common Factor of 498,734,403 using Euclid's algorithm

Highest Common Factor of 498,734,403 is 1

Step 1: Since 734 > 498, we apply the division lemma to 734 and 498, to get

734 = 498 x 1 + 236

Step 2: Since the reminder 498 ≠ 0, we apply division lemma to 236 and 498, to get

498 = 236 x 2 + 26

Step 3: We consider the new divisor 236 and the new remainder 26, and apply the division lemma to get

236 = 26 x 9 + 2

We consider the new divisor 26 and the new remainder 2, and apply the division lemma to get

26 = 2 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 498 and 734 is 2

Notice that 2 = HCF(26,2) = HCF(236,26) = HCF(498,236) = HCF(734,498) .

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

Step 1: Since 403 > 2, we apply the division lemma to 403 and 2, to get

403 = 2 x 201 + 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 403 is 1

Notice that 1 = HCF(2,1) = HCF(403,2) .

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Frequently Asked Questions on HCF of 498, 734, 403 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, 734, 403?

Answer: HCF of 498, 734, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 498, 734, 403 using Euclid's Algorithm?

Answer: For arbitrary numbers 498, 734, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.