Highest Common Factor of 638, 442, 43 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 638, 442, 43 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 638, 442, 43 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 638, 442, 43 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 638, 442, 43 is 1.

HCF(638, 442, 43) = 1

HCF of 638, 442, 43 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 638, 442, 43 is 1.

Highest Common Factor of 638,442,43 using Euclid's algorithm

Highest Common Factor of 638,442,43 is 1

Step 1: Since 638 > 442, we apply the division lemma to 638 and 442, to get

638 = 442 x 1 + 196

Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 196 and 442, to get

442 = 196 x 2 + 50

Step 3: We consider the new divisor 196 and the new remainder 50, and apply the division lemma to get

196 = 50 x 3 + 46

We consider the new divisor 50 and the new remainder 46,and apply the division lemma to get

50 = 46 x 1 + 4

We consider the new divisor 46 and the new remainder 4,and apply the division lemma to get

46 = 4 x 11 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 638 and 442 is 2

Notice that 2 = HCF(4,2) = HCF(46,4) = HCF(50,46) = HCF(196,50) = HCF(442,196) = HCF(638,442) .

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

Step 1: Since 43 > 2, we apply the division lemma to 43 and 2, to get

43 = 2 x 21 + 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 43 is 1

Notice that 1 = HCF(2,1) = HCF(43,2) .

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Frequently Asked Questions on HCF of 638, 442, 43 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 638, 442, 43?

Answer: HCF of 638, 442, 43 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 638, 442, 43 using Euclid's Algorithm?

Answer: For arbitrary numbers 638, 442, 43 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.