Highest Common Factor of 121, 678, 418 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 121, 678, 418 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 121, 678, 418 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 121, 678, 418 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 121, 678, 418 is 1.

HCF(121, 678, 418) = 1

HCF of 121, 678, 418 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 121, 678, 418 is 1.

Highest Common Factor of 121,678,418 using Euclid's algorithm

Highest Common Factor of 121,678,418 is 1

Step 1: Since 678 > 121, we apply the division lemma to 678 and 121, to get

678 = 121 x 5 + 73

Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 73 and 121, to get

121 = 73 x 1 + 48

Step 3: We consider the new divisor 73 and the new remainder 48, and apply the division lemma to get

73 = 48 x 1 + 25

We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get

48 = 25 x 1 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 121 and 678 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(73,48) = HCF(121,73) = HCF(678,121) .

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

Step 1: Since 418 > 1, we apply the division lemma to 418 and 1, to get

418 = 1 x 418 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 418 is 1

Notice that 1 = HCF(418,1) .

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Frequently Asked Questions on HCF of 121, 678, 418 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 121, 678, 418?

Answer: HCF of 121, 678, 418 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 121, 678, 418 using Euclid's Algorithm?

Answer: For arbitrary numbers 121, 678, 418 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.