Highest Common Factor of 411, 644, 689 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 411, 644, 689 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 411, 644, 689 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 411, 644, 689 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 411, 644, 689 is 1.

HCF(411, 644, 689) = 1

HCF of 411, 644, 689 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 411, 644, 689 is 1.

Highest Common Factor of 411,644,689 using Euclid's algorithm

Highest Common Factor of 411,644,689 is 1

Step 1: Since 644 > 411, we apply the division lemma to 644 and 411, to get

644 = 411 x 1 + 233

Step 2: Since the reminder 411 ≠ 0, we apply division lemma to 233 and 411, to get

411 = 233 x 1 + 178

Step 3: We consider the new divisor 233 and the new remainder 178, and apply the division lemma to get

233 = 178 x 1 + 55

We consider the new divisor 178 and the new remainder 55,and apply the division lemma to get

178 = 55 x 3 + 13

We consider the new divisor 55 and the new remainder 13,and apply the division lemma to get

55 = 13 x 4 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 411 and 644 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(55,13) = HCF(178,55) = HCF(233,178) = HCF(411,233) = HCF(644,411) .

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

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

689 = 1 x 689 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 689 is 1

Notice that 1 = HCF(689,1) .

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Frequently Asked Questions on HCF of 411, 644, 689 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 411, 644, 689?

Answer: HCF of 411, 644, 689 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 411, 644, 689 using Euclid's Algorithm?

Answer: For arbitrary numbers 411, 644, 689 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.