Highest Common Factor of 497, 668, 251 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 497, 668, 251 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 497, 668, 251 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 497, 668, 251 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 497, 668, 251 is 1.

HCF(497, 668, 251) = 1

HCF of 497, 668, 251 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 497, 668, 251 is 1.

Highest Common Factor of 497,668,251 using Euclid's algorithm

Highest Common Factor of 497,668,251 is 1

Step 1: Since 668 > 497, we apply the division lemma to 668 and 497, to get

668 = 497 x 1 + 171

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 171 and 497, to get

497 = 171 x 2 + 155

Step 3: We consider the new divisor 171 and the new remainder 155, and apply the division lemma to get

171 = 155 x 1 + 16

We consider the new divisor 155 and the new remainder 16,and apply the division lemma to get

155 = 16 x 9 + 11

We consider the new divisor 16 and the new remainder 11,and apply the division lemma to get

16 = 11 x 1 + 5

We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get

11 = 5 x 2 + 1

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 497 and 668 is 1

Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(16,11) = HCF(155,16) = HCF(171,155) = HCF(497,171) = HCF(668,497) .

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

Step 1: Since 251 > 1, we apply the division lemma to 251 and 1, to get

251 = 1 x 251 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 251 is 1

Notice that 1 = HCF(251,1) .

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Frequently Asked Questions on HCF of 497, 668, 251 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 497, 668, 251?

Answer: HCF of 497, 668, 251 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 497, 668, 251 using Euclid's Algorithm?

Answer: For arbitrary numbers 497, 668, 251 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.