Highest Common Factor of 616, 182, 121 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 616, 182, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 616, 182, 121 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 616, 182, 121 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 616, 182, 121 is 1.

HCF(616, 182, 121) = 1

HCF of 616, 182, 121 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 616, 182, 121 is 1.

Highest Common Factor of 616,182,121 using Euclid's algorithm

Highest Common Factor of 616,182,121 is 1

Step 1: Since 616 > 182, we apply the division lemma to 616 and 182, to get

616 = 182 x 3 + 70

Step 2: Since the reminder 182 ≠ 0, we apply division lemma to 70 and 182, to get

182 = 70 x 2 + 42

Step 3: We consider the new divisor 70 and the new remainder 42, and apply the division lemma to get

70 = 42 x 1 + 28

We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get

42 = 28 x 1 + 14

We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get

28 = 14 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 616 and 182 is 14

Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(70,42) = HCF(182,70) = HCF(616,182) .

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

Step 1: Since 121 > 14, we apply the division lemma to 121 and 14, to get

121 = 14 x 8 + 9

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 9 and 14, to get

14 = 9 x 1 + 5

Step 3: We consider the new divisor 9 and the new remainder 5, and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 14 and 121 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(121,14) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 616, 182, 121 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 616, 182, 121?

Answer: HCF of 616, 182, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 616, 182, 121 using Euclid's Algorithm?

Answer: For arbitrary numbers 616, 182, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.