Highest Common Factor of 397, 542, 138 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 397, 542, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 397, 542, 138 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 397, 542, 138 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 397, 542, 138 is 1.

HCF(397, 542, 138) = 1

HCF of 397, 542, 138 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 397, 542, 138 is 1.

Highest Common Factor of 397,542,138 using Euclid's algorithm

Highest Common Factor of 397,542,138 is 1

Step 1: Since 542 > 397, we apply the division lemma to 542 and 397, to get

542 = 397 x 1 + 145

Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 145 and 397, to get

397 = 145 x 2 + 107

Step 3: We consider the new divisor 145 and the new remainder 107, and apply the division lemma to get

145 = 107 x 1 + 38

We consider the new divisor 107 and the new remainder 38,and apply the division lemma to get

107 = 38 x 2 + 31

We consider the new divisor 38 and the new remainder 31,and apply the division lemma to get

38 = 31 x 1 + 7

We consider the new divisor 31 and the new remainder 7,and apply the division lemma to get

31 = 7 x 4 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 397 and 542 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(31,7) = HCF(38,31) = HCF(107,38) = HCF(145,107) = HCF(397,145) = HCF(542,397) .

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

Step 1: Since 138 > 1, we apply the division lemma to 138 and 1, to get

138 = 1 x 138 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 138 is 1

Notice that 1 = HCF(138,1) .

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Frequently Asked Questions on HCF of 397, 542, 138 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 397, 542, 138?

Answer: HCF of 397, 542, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 397, 542, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 397, 542, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.