Highest Common Factor of 455, 130, 351 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 455, 130, 351 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 455, 130, 351 is 13 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 455, 130, 351 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 455, 130, 351 is 13.

HCF(455, 130, 351) = 13

HCF of 455, 130, 351 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 455, 130, 351 is 13.

Highest Common Factor of 455,130,351 using Euclid's algorithm

Highest Common Factor of 455,130,351 is 13

Step 1: Since 455 > 130, we apply the division lemma to 455 and 130, to get

455 = 130 x 3 + 65

Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 65 and 130, to get

130 = 65 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 455 and 130 is 65

Notice that 65 = HCF(130,65) = HCF(455,130) .

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

Step 1: Since 351 > 65, we apply the division lemma to 351 and 65, to get

351 = 65 x 5 + 26

Step 2: Since the reminder 65 ≠ 0, we apply division lemma to 26 and 65, to get

65 = 26 x 2 + 13

Step 3: We consider the new divisor 26 and the new remainder 13, and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 65 and 351 is 13

Notice that 13 = HCF(26,13) = HCF(65,26) = HCF(351,65) .

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Frequently Asked Questions on HCF of 455, 130, 351 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 455, 130, 351?

Answer: HCF of 455, 130, 351 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 455, 130, 351 using Euclid's Algorithm?

Answer: For arbitrary numbers 455, 130, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.