Highest Common Factor of 689, 543, 602 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 689, 543, 602 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 689, 543, 602 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 689, 543, 602 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 689, 543, 602 is 1.

HCF(689, 543, 602) = 1

HCF of 689, 543, 602 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 689, 543, 602 is 1.

Highest Common Factor of 689,543,602 using Euclid's algorithm

Highest Common Factor of 689,543,602 is 1

Step 1: Since 689 > 543, we apply the division lemma to 689 and 543, to get

689 = 543 x 1 + 146

Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 146 and 543, to get

543 = 146 x 3 + 105

Step 3: We consider the new divisor 146 and the new remainder 105, and apply the division lemma to get

146 = 105 x 1 + 41

We consider the new divisor 105 and the new remainder 41,and apply the division lemma to get

105 = 41 x 2 + 23

We consider the new divisor 41 and the new remainder 23,and apply the division lemma to get

41 = 23 x 1 + 18

We consider the new divisor 23 and the new remainder 18,and apply the division lemma to get

23 = 18 x 1 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 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 689 and 543 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(23,18) = HCF(41,23) = HCF(105,41) = HCF(146,105) = HCF(543,146) = HCF(689,543) .

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

Step 1: Since 602 > 1, we apply the division lemma to 602 and 1, to get

602 = 1 x 602 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 602 is 1

Notice that 1 = HCF(602,1) .

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Frequently Asked Questions on HCF of 689, 543, 602 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 689, 543, 602?

Answer: HCF of 689, 543, 602 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 689, 543, 602 using Euclid's Algorithm?

Answer: For arbitrary numbers 689, 543, 602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.