Highest Common Factor of 736, 108, 83 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 736, 108, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 736, 108, 83 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 736, 108, 83 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 736, 108, 83 is 1.

HCF(736, 108, 83) = 1

HCF of 736, 108, 83 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 736, 108, 83 is 1.

Highest Common Factor of 736,108,83 using Euclid's algorithm

Highest Common Factor of 736,108,83 is 1

Step 1: Since 736 > 108, we apply the division lemma to 736 and 108, to get

736 = 108 x 6 + 88

Step 2: Since the reminder 108 ≠ 0, we apply division lemma to 88 and 108, to get

108 = 88 x 1 + 20

Step 3: We consider the new divisor 88 and the new remainder 20, and apply the division lemma to get

88 = 20 x 4 + 8

We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get

20 = 8 x 2 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 736 and 108 is 4

Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(88,20) = HCF(108,88) = HCF(736,108) .


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

Step 1: Since 83 > 4, we apply the division lemma to 83 and 4, to get

83 = 4 x 20 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 83 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(83,4) .

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Frequently Asked Questions on HCF of 736, 108, 83 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 736, 108, 83?

Answer: HCF of 736, 108, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 736, 108, 83 using Euclid's Algorithm?

Answer: For arbitrary numbers 736, 108, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.