Highest Common Factor of 129, 402, 190 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 129, 402, 190 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 129, 402, 190 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 129, 402, 190 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 129, 402, 190 is 1.

HCF(129, 402, 190) = 1

HCF of 129, 402, 190 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 129, 402, 190 is 1.

Highest Common Factor of 129,402,190 using Euclid's algorithm

Highest Common Factor of 129,402,190 is 1

Step 1: Since 402 > 129, we apply the division lemma to 402 and 129, to get

402 = 129 x 3 + 15

Step 2: Since the reminder 129 ≠ 0, we apply division lemma to 15 and 129, to get

129 = 15 x 8 + 9

Step 3: We consider the new divisor 15 and the new remainder 9, and apply the division lemma to get

15 = 9 x 1 + 6

We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get

9 = 6 x 1 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 129 and 402 is 3

Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(129,15) = HCF(402,129) .

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

Step 1: Since 190 > 3, we apply the division lemma to 190 and 3, to get

190 = 3 x 63 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 190 is 1

Notice that 1 = HCF(3,1) = HCF(190,3) .

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Frequently Asked Questions on HCF of 129, 402, 190 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 129, 402, 190?

Answer: HCF of 129, 402, 190 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 129, 402, 190 using Euclid's Algorithm?

Answer: For arbitrary numbers 129, 402, 190 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.