Highest Common Factor of 737, 331, 660, 56 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 737, 331, 660, 56 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 737, 331, 660, 56 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 737, 331, 660, 56 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 737, 331, 660, 56 is 1.

HCF(737, 331, 660, 56) = 1

HCF of 737, 331, 660, 56 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 737, 331, 660, 56 is 1.

Highest Common Factor of 737,331,660,56 using Euclid's algorithm

Highest Common Factor of 737,331,660,56 is 1

Step 1: Since 737 > 331, we apply the division lemma to 737 and 331, to get

737 = 331 x 2 + 75

Step 2: Since the reminder 331 ≠ 0, we apply division lemma to 75 and 331, to get

331 = 75 x 4 + 31

Step 3: We consider the new divisor 75 and the new remainder 31, and apply the division lemma to get

75 = 31 x 2 + 13

We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get

31 = 13 x 2 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 737 and 331 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(75,31) = HCF(331,75) = HCF(737,331) .

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

Step 1: Since 660 > 1, we apply the division lemma to 660 and 1, to get

660 = 1 x 660 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 660 is 1

Notice that 1 = HCF(660,1) .

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

Step 1: Since 56 > 1, we apply the division lemma to 56 and 1, to get

56 = 1 x 56 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 56 is 1

Notice that 1 = HCF(56,1) .

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Frequently Asked Questions on HCF of 737, 331, 660, 56 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 737, 331, 660, 56?

Answer: HCF of 737, 331, 660, 56 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 737, 331, 660, 56 using Euclid's Algorithm?

Answer: For arbitrary numbers 737, 331, 660, 56 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.