Highest Common Factor of 299, 377 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 299, 377 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 299, 377 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 299, 377 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 299, 377 is 13.

HCF(299, 377) = 13

HCF of 299, 377 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 299, 377 is 13.

Highest Common Factor of 299,377 using Euclid's algorithm

Highest Common Factor of 299,377 is 13

Step 1: Since 377 > 299, we apply the division lemma to 377 and 299, to get

377 = 299 x 1 + 78

Step 2: Since the reminder 299 ≠ 0, we apply division lemma to 78 and 299, to get

299 = 78 x 3 + 65

Step 3: We consider the new divisor 78 and the new remainder 65, and apply the division lemma to get

78 = 65 x 1 + 13

We consider the new divisor 65 and the new remainder 13, and apply the division lemma to get

65 = 13 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 299 and 377 is 13

Notice that 13 = HCF(65,13) = HCF(78,65) = HCF(299,78) = HCF(377,299) .

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Frequently Asked Questions on HCF of 299, 377 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 299, 377?

Answer: HCF of 299, 377 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 299, 377 using Euclid's Algorithm?

Answer: For arbitrary numbers 299, 377 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.