Highest Common Factor of 635, 390, 130 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 635, 390, 130 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 635, 390, 130 is 5 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 635, 390, 130 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 635, 390, 130 is 5.

HCF(635, 390, 130) = 5

HCF of 635, 390, 130 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 635, 390, 130 is 5.

Highest Common Factor of 635,390,130 using Euclid's algorithm

Highest Common Factor of 635,390,130 is 5

Step 1: Since 635 > 390, we apply the division lemma to 635 and 390, to get

635 = 390 x 1 + 245

Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 245 and 390, to get

390 = 245 x 1 + 145

Step 3: We consider the new divisor 245 and the new remainder 145, and apply the division lemma to get

245 = 145 x 1 + 100

We consider the new divisor 145 and the new remainder 100,and apply the division lemma to get

145 = 100 x 1 + 45

We consider the new divisor 100 and the new remainder 45,and apply the division lemma to get

100 = 45 x 2 + 10

We consider the new divisor 45 and the new remainder 10,and apply the division lemma to get

45 = 10 x 4 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 635 and 390 is 5

Notice that 5 = HCF(10,5) = HCF(45,10) = HCF(100,45) = HCF(145,100) = HCF(245,145) = HCF(390,245) = HCF(635,390) .

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

Step 1: Since 130 > 5, we apply the division lemma to 130 and 5, to get

130 = 5 x 26 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 130 is 5

Notice that 5 = HCF(130,5) .

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Frequently Asked Questions on HCF of 635, 390, 130 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 635, 390, 130?

Answer: HCF of 635, 390, 130 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 635, 390, 130 using Euclid's Algorithm?

Answer: For arbitrary numbers 635, 390, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.