Highest Common Factor of 643, 761, 342 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 643, 761, 342 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 643, 761, 342 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 643, 761, 342 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 643, 761, 342 is 1.

HCF(643, 761, 342) = 1

HCF of 643, 761, 342 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 643, 761, 342 is 1.

Highest Common Factor of 643,761,342 using Euclid's algorithm

Highest Common Factor of 643,761,342 is 1

Step 1: Since 761 > 643, we apply the division lemma to 761 and 643, to get

761 = 643 x 1 + 118

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 118 and 643, to get

643 = 118 x 5 + 53

Step 3: We consider the new divisor 118 and the new remainder 53, and apply the division lemma to get

118 = 53 x 2 + 12

We consider the new divisor 53 and the new remainder 12,and apply the division lemma to get

53 = 12 x 4 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 643 and 761 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(53,12) = HCF(118,53) = HCF(643,118) = HCF(761,643) .

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

Step 1: Since 342 > 1, we apply the division lemma to 342 and 1, to get

342 = 1 x 342 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 342 is 1

Notice that 1 = HCF(342,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 643, 761, 342 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 643, 761, 342?

Answer: HCF of 643, 761, 342 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 643, 761, 342 using Euclid's Algorithm?

Answer: For arbitrary numbers 643, 761, 342 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.