Highest Common Factor of 409, 671, 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 409, 671, 138 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 409, 671, 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 409, 671, 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 409, 671, 138 is 1.

HCF(409, 671, 138) = 1

HCF of 409, 671, 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 409, 671, 138 is 1.

Highest Common Factor of 409,671,138 using Euclid's algorithm

Highest Common Factor of 409,671,138 is 1

Step 1: Since 671 > 409, we apply the division lemma to 671 and 409, to get

671 = 409 x 1 + 262

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 262 and 409, to get

409 = 262 x 1 + 147

Step 3: We consider the new divisor 262 and the new remainder 147, and apply the division lemma to get

262 = 147 x 1 + 115

We consider the new divisor 147 and the new remainder 115,and apply the division lemma to get

147 = 115 x 1 + 32

We consider the new divisor 115 and the new remainder 32,and apply the division lemma to get

115 = 32 x 3 + 19

We consider the new divisor 32 and the new remainder 19,and apply the division lemma to get

32 = 19 x 1 + 13

We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get

19 = 13 x 1 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 409 and 671 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(32,19) = HCF(115,32) = HCF(147,115) = HCF(262,147) = HCF(409,262) = HCF(671,409) .

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 409, 671, 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 409, 671, 138?

Answer: HCF of 409, 671, 138 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 409, 671, 138 using Euclid's Algorithm?

Answer: For arbitrary numbers 409, 671, 138 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.