Highest Common Factor of 313, 138, 476 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 313, 138, 476 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 313, 138, 476 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 313, 138, 476 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 313, 138, 476 is 1.

HCF(313, 138, 476) = 1

HCF of 313, 138, 476 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 313, 138, 476 is 1.

Highest Common Factor of 313,138,476 using Euclid's algorithm

Highest Common Factor of 313,138,476 is 1

Step 1: Since 313 > 138, we apply the division lemma to 313 and 138, to get

313 = 138 x 2 + 37

Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 37 and 138, to get

138 = 37 x 3 + 27

Step 3: We consider the new divisor 37 and the new remainder 27, and apply the division lemma to get

37 = 27 x 1 + 10

We consider the new divisor 27 and the new remainder 10,and apply the division lemma to get

27 = 10 x 2 + 7

We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get

10 = 7 x 1 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 313 and 138 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(27,10) = HCF(37,27) = HCF(138,37) = HCF(313,138) .

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

Step 1: Since 476 > 1, we apply the division lemma to 476 and 1, to get

476 = 1 x 476 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 476 is 1

Notice that 1 = HCF(476,1) .

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Frequently Asked Questions on HCF of 313, 138, 476 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 313, 138, 476?

Answer: HCF of 313, 138, 476 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 313, 138, 476 using Euclid's Algorithm?

Answer: For arbitrary numbers 313, 138, 476 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.