Highest Common Factor of 310, 7316, 1471 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, 7316, 1471 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 7316, 1471 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 310, 7316, 1471 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, 7316, 1471 is 1.

HCF(310, 7316, 1471) = 1

HCF of 310, 7316, 1471 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, 7316, 1471 is 1.

Highest Common Factor of 310,7316,1471 using Euclid's algorithm

Highest Common Factor of 310,7316,1471 is 1

Step 1: Since 7316 > 310, we apply the division lemma to 7316 and 310, to get

7316 = 310 x 23 + 186

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 186 and 310, to get

310 = 186 x 1 + 124

Step 3: We consider the new divisor 186 and the new remainder 124, and apply the division lemma to get

186 = 124 x 1 + 62

We consider the new divisor 124 and the new remainder 62, and apply the division lemma to get

124 = 62 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 62, the HCF of 310 and 7316 is 62

Notice that 62 = HCF(124,62) = HCF(186,124) = HCF(310,186) = HCF(7316,310) .

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

Step 1: Since 1471 > 62, we apply the division lemma to 1471 and 62, to get

1471 = 62 x 23 + 45

Step 2: Since the reminder 62 ≠ 0, we apply division lemma to 45 and 62, to get

62 = 45 x 1 + 17

Step 3: We consider the new divisor 45 and the new remainder 17, and apply the division lemma to get

45 = 17 x 2 + 11

We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get

17 = 11 x 1 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 62 and 1471 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(62,45) = HCF(1471,62) .

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Frequently Asked Questions on HCF of 310, 7316, 1471 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, 7316, 1471?

Answer: HCF of 310, 7316, 1471 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 7316, 1471 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 7316, 1471 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.