Highest Common Factor of 654, 341, 112 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 654, 341, 112 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 654, 341, 112 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 654, 341, 112 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 654, 341, 112 is 1.

HCF(654, 341, 112) = 1

HCF of 654, 341, 112 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 654, 341, 112 is 1.

Highest Common Factor of 654,341,112 using Euclid's algorithm

Highest Common Factor of 654,341,112 is 1

Step 1: Since 654 > 341, we apply the division lemma to 654 and 341, to get

654 = 341 x 1 + 313

Step 2: Since the reminder 341 ≠ 0, we apply division lemma to 313 and 341, to get

341 = 313 x 1 + 28

Step 3: We consider the new divisor 313 and the new remainder 28, and apply the division lemma to get

313 = 28 x 11 + 5

We consider the new divisor 28 and the new remainder 5,and apply the division lemma to get

28 = 5 x 5 + 3

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

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 654 and 341 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(28,5) = HCF(313,28) = HCF(341,313) = HCF(654,341) .

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

Step 1: Since 112 > 1, we apply the division lemma to 112 and 1, to get

112 = 1 x 112 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 112 is 1

Notice that 1 = HCF(112,1) .

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Frequently Asked Questions on HCF of 654, 341, 112 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 654, 341, 112?

Answer: HCF of 654, 341, 112 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 654, 341, 112 using Euclid's Algorithm?

Answer: For arbitrary numbers 654, 341, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.