Highest Common Factor of 310, 476, 278 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 310, 476, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 476, 278 is 2 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 310, 476, 278 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 310, 476, 278 is 2.

HCF(310, 476, 278) = 2

HCF of 310, 476, 278 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 310, 476, 278 is 2.

Highest Common Factor of 310,476,278 using Euclid's algorithm

Highest Common Factor of 310,476,278 is 2

Step 1: Since 476 > 310, we apply the division lemma to 476 and 310, to get

476 = 310 x 1 + 166

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 166 and 310, to get

310 = 166 x 1 + 144

Step 3: We consider the new divisor 166 and the new remainder 144, and apply the division lemma to get

166 = 144 x 1 + 22

We consider the new divisor 144 and the new remainder 22,and apply the division lemma to get

144 = 22 x 6 + 12

We consider the new divisor 22 and the new remainder 12,and apply the division lemma to get

22 = 12 x 1 + 10

We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get

12 = 10 x 1 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 476 is 2

Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(22,12) = HCF(144,22) = HCF(166,144) = HCF(310,166) = HCF(476,310) .

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

Step 1: Since 278 > 2, we apply the division lemma to 278 and 2, to get

278 = 2 x 139 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 278 is 2

Notice that 2 = HCF(278,2) .

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Frequently Asked Questions on HCF of 310, 476, 278 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 310, 476, 278?

Answer: HCF of 310, 476, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 476, 278 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 476, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.