Highest Common Factor of 916, 119, 184 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 916, 119, 184 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 916, 119, 184 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 916, 119, 184 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 916, 119, 184 is 1.

HCF(916, 119, 184) = 1

HCF of 916, 119, 184 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 916, 119, 184 is 1.

Highest Common Factor of 916,119,184 using Euclid's algorithm

Highest Common Factor of 916,119,184 is 1

Step 1: Since 916 > 119, we apply the division lemma to 916 and 119, to get

916 = 119 x 7 + 83

Step 2: Since the reminder 119 ≠ 0, we apply division lemma to 83 and 119, to get

119 = 83 x 1 + 36

Step 3: We consider the new divisor 83 and the new remainder 36, and apply the division lemma to get

83 = 36 x 2 + 11

We consider the new divisor 36 and the new remainder 11,and apply the division lemma to get

36 = 11 x 3 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 916 and 119 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(36,11) = HCF(83,36) = HCF(119,83) = HCF(916,119) .

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

Step 1: Since 184 > 1, we apply the division lemma to 184 and 1, to get

184 = 1 x 184 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 184 is 1

Notice that 1 = HCF(184,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 916, 119, 184 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 916, 119, 184?

Answer: HCF of 916, 119, 184 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 916, 119, 184 using Euclid's Algorithm?

Answer: For arbitrary numbers 916, 119, 184 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.