Highest Common Factor of 96, 332, 119 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 96, 332, 119 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 96, 332, 119 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 96, 332, 119 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 96, 332, 119 is 1.

HCF(96, 332, 119) = 1

HCF of 96, 332, 119 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 96, 332, 119 is 1.

Highest Common Factor of 96,332,119 using Euclid's algorithm

Highest Common Factor of 96,332,119 is 1

Step 1: Since 332 > 96, we apply the division lemma to 332 and 96, to get

332 = 96 x 3 + 44

Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 44 and 96, to get

96 = 44 x 2 + 8

Step 3: We consider the new divisor 44 and the new remainder 8, and apply the division lemma to get

44 = 8 x 5 + 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 96 and 332 is 4

Notice that 4 = HCF(8,4) = HCF(44,8) = HCF(96,44) = HCF(332,96) .

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

Step 1: Since 119 > 4, we apply the division lemma to 119 and 4, to get

119 = 4 x 29 + 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 119 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(119,4) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 96, 332, 119 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 96, 332, 119?

Answer: HCF of 96, 332, 119 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 96, 332, 119 using Euclid's Algorithm?

Answer: For arbitrary numbers 96, 332, 119 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.