Highest Common Factor of 412, 634, 260, 13 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 412, 634, 260, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 634, 260, 13 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 412, 634, 260, 13 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 412, 634, 260, 13 is 1.

HCF(412, 634, 260, 13) = 1

HCF of 412, 634, 260, 13 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 412, 634, 260, 13 is 1.

Highest Common Factor of 412,634,260,13 using Euclid's algorithm

Highest Common Factor of 412,634,260,13 is 1

Step 1: Since 634 > 412, we apply the division lemma to 634 and 412, to get

634 = 412 x 1 + 222

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 222 and 412, to get

412 = 222 x 1 + 190

Step 3: We consider the new divisor 222 and the new remainder 190, and apply the division lemma to get

222 = 190 x 1 + 32

We consider the new divisor 190 and the new remainder 32,and apply the division lemma to get

190 = 32 x 5 + 30

We consider the new divisor 32 and the new remainder 30,and apply the division lemma to get

32 = 30 x 1 + 2

We consider the new divisor 30 and the new remainder 2,and apply the division lemma to get

30 = 2 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 412 and 634 is 2

Notice that 2 = HCF(30,2) = HCF(32,30) = HCF(190,32) = HCF(222,190) = HCF(412,222) = HCF(634,412) .

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

Step 1: Since 260 > 2, we apply the division lemma to 260 and 2, to get

260 = 2 x 130 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 260 is 2

Notice that 2 = HCF(260,2) .

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

Step 1: Since 13 > 2, we apply the division lemma to 13 and 2, to get

13 = 2 x 6 + 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 13 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) .

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Frequently Asked Questions on HCF of 412, 634, 260, 13 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 412, 634, 260, 13?

Answer: HCF of 412, 634, 260, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 634, 260, 13 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 634, 260, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.