Highest Common Factor of 168, 9122, 1696 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 168, 9122, 1696 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 168, 9122, 1696 is 2 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 168, 9122, 1696 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 168, 9122, 1696 is 2.

HCF(168, 9122, 1696) = 2

HCF of 168, 9122, 1696 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 168, 9122, 1696 is 2.

Highest Common Factor of 168,9122,1696 using Euclid's algorithm

Highest Common Factor of 168,9122,1696 is 2

Step 1: Since 9122 > 168, we apply the division lemma to 9122 and 168, to get

9122 = 168 x 54 + 50

Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 50 and 168, to get

168 = 50 x 3 + 18

Step 3: We consider the new divisor 50 and the new remainder 18, and apply the division lemma to get

50 = 18 x 2 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 168 and 9122 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(50,18) = HCF(168,50) = HCF(9122,168) .

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

Step 1: Since 1696 > 2, we apply the division lemma to 1696 and 2, to get

1696 = 2 x 848 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 1696 is 2

Notice that 2 = HCF(1696,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 168, 9122, 1696 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 168, 9122, 1696?

Answer: HCF of 168, 9122, 1696 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 168, 9122, 1696 using Euclid's Algorithm?

Answer: For arbitrary numbers 168, 9122, 1696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.