Highest Common Factor of 747, 310, 332 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 747, 310, 332 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 747, 310, 332 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 747, 310, 332 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 747, 310, 332 is 1.

HCF(747, 310, 332) = 1

HCF of 747, 310, 332 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 747, 310, 332 is 1.

Highest Common Factor of 747,310,332 using Euclid's algorithm

Highest Common Factor of 747,310,332 is 1

Step 1: Since 747 > 310, we apply the division lemma to 747 and 310, to get

747 = 310 x 2 + 127

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 127 and 310, to get

310 = 127 x 2 + 56

Step 3: We consider the new divisor 127 and the new remainder 56, and apply the division lemma to get

127 = 56 x 2 + 15

We consider the new divisor 56 and the new remainder 15,and apply the division lemma to get

56 = 15 x 3 + 11

We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get

15 = 11 x 1 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 747 and 310 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(56,15) = HCF(127,56) = HCF(310,127) = HCF(747,310) .

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

Step 1: Since 332 > 1, we apply the division lemma to 332 and 1, to get

332 = 1 x 332 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 332 is 1

Notice that 1 = HCF(332,1) .

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Frequently Asked Questions on HCF of 747, 310, 332 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 747, 310, 332?

Answer: HCF of 747, 310, 332 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 747, 310, 332 using Euclid's Algorithm?

Answer: For arbitrary numbers 747, 310, 332 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.