Highest Common Factor of 377, 988, 208 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 377, 988, 208 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 377, 988, 208 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 377, 988, 208 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 377, 988, 208 is 13.

HCF(377, 988, 208) = 13

HCF of 377, 988, 208 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 377, 988, 208 is 13.

Highest Common Factor of 377,988,208 using Euclid's algorithm

Highest Common Factor of 377,988,208 is 13

Step 1: Since 988 > 377, we apply the division lemma to 988 and 377, to get

988 = 377 x 2 + 234

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 234 and 377, to get

377 = 234 x 1 + 143

Step 3: We consider the new divisor 234 and the new remainder 143, and apply the division lemma to get

234 = 143 x 1 + 91

We consider the new divisor 143 and the new remainder 91,and apply the division lemma to get

143 = 91 x 1 + 52

We consider the new divisor 91 and the new remainder 52,and apply the division lemma to get

91 = 52 x 1 + 39

We consider the new divisor 52 and the new remainder 39,and apply the division lemma to get

52 = 39 x 1 + 13

We consider the new divisor 39 and the new remainder 13,and apply the division lemma to get

39 = 13 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 377 and 988 is 13

Notice that 13 = HCF(39,13) = HCF(52,39) = HCF(91,52) = HCF(143,91) = HCF(234,143) = HCF(377,234) = HCF(988,377) .

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

Step 1: Since 208 > 13, we apply the division lemma to 208 and 13, to get

208 = 13 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 13 and 208 is 13

Notice that 13 = HCF(208,13) .

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Frequently Asked Questions on HCF of 377, 988, 208 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 377, 988, 208?

Answer: HCF of 377, 988, 208 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 377, 988, 208 using Euclid's Algorithm?

Answer: For arbitrary numbers 377, 988, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.