Highest Common Factor of 168, 278, 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 168, 278, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 168, 278, 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 168, 278, 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 168, 278, 121 is 1.

HCF(168, 278, 121) = 1

HCF of 168, 278, 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 168, 278, 121 is 1.

Highest Common Factor of 168,278,121 using Euclid's algorithm

Highest Common Factor of 168,278,121 is 1

Step 1: Since 278 > 168, we apply the division lemma to 278 and 168, to get

278 = 168 x 1 + 110

Step 2: Since the reminder 168 ≠ 0, we apply division lemma to 110 and 168, to get

168 = 110 x 1 + 58

Step 3: We consider the new divisor 110 and the new remainder 58, and apply the division lemma to get

110 = 58 x 1 + 52

We consider the new divisor 58 and the new remainder 52,and apply the division lemma to get

58 = 52 x 1 + 6

We consider the new divisor 52 and the new remainder 6,and apply the division lemma to get

52 = 6 x 8 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 278 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(52,6) = HCF(58,52) = HCF(110,58) = HCF(168,110) = HCF(278,168) .

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

Step 1: Since 121 > 2, we apply the division lemma to 121 and 2, to get

121 = 2 x 60 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 121 is 1

Notice that 1 = HCF(2,1) = HCF(121,2) .

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Frequently Asked Questions on HCF of 168, 278, 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 168, 278, 121?

Answer: HCF of 168, 278, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 168, 278, 121 using Euclid's Algorithm?

Answer: For arbitrary numbers 168, 278, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.