Highest Common Factor of 418, 670, 641 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 418, 670, 641 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 418, 670, 641 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 418, 670, 641 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 418, 670, 641 is 1.

HCF(418, 670, 641) = 1

HCF of 418, 670, 641 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 418, 670, 641 is 1.

Highest Common Factor of 418,670,641 using Euclid's algorithm

Highest Common Factor of 418,670,641 is 1

Step 1: Since 670 > 418, we apply the division lemma to 670 and 418, to get

670 = 418 x 1 + 252

Step 2: Since the reminder 418 ≠ 0, we apply division lemma to 252 and 418, to get

418 = 252 x 1 + 166

Step 3: We consider the new divisor 252 and the new remainder 166, and apply the division lemma to get

252 = 166 x 1 + 86

We consider the new divisor 166 and the new remainder 86,and apply the division lemma to get

166 = 86 x 1 + 80

We consider the new divisor 86 and the new remainder 80,and apply the division lemma to get

86 = 80 x 1 + 6

We consider the new divisor 80 and the new remainder 6,and apply the division lemma to get

80 = 6 x 13 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 418 and 670 is 2

Notice that 2 = HCF(6,2) = HCF(80,6) = HCF(86,80) = HCF(166,86) = HCF(252,166) = HCF(418,252) = HCF(670,418) .

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

Step 1: Since 641 > 2, we apply the division lemma to 641 and 2, to get

641 = 2 x 320 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 641 is 1

Notice that 1 = HCF(2,1) = HCF(641,2) .

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Frequently Asked Questions on HCF of 418, 670, 641 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 418, 670, 641?

Answer: HCF of 418, 670, 641 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 418, 670, 641 using Euclid's Algorithm?

Answer: For arbitrary numbers 418, 670, 641 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.