Highest Common Factor of 610, 225, 107 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 610, 225, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 610, 225, 107 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 610, 225, 107 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 610, 225, 107 is 1.

HCF(610, 225, 107) = 1

HCF of 610, 225, 107 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 610, 225, 107 is 1.

Highest Common Factor of 610,225,107 using Euclid's algorithm

Highest Common Factor of 610,225,107 is 1

Step 1: Since 610 > 225, we apply the division lemma to 610 and 225, to get

610 = 225 x 2 + 160

Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 160 and 225, to get

225 = 160 x 1 + 65

Step 3: We consider the new divisor 160 and the new remainder 65, and apply the division lemma to get

160 = 65 x 2 + 30

We consider the new divisor 65 and the new remainder 30,and apply the division lemma to get

65 = 30 x 2 + 5

We consider the new divisor 30 and the new remainder 5,and apply the division lemma to get

30 = 5 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 610 and 225 is 5

Notice that 5 = HCF(30,5) = HCF(65,30) = HCF(160,65) = HCF(225,160) = HCF(610,225) .

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

Step 1: Since 107 > 5, we apply the division lemma to 107 and 5, to get

107 = 5 x 21 + 2

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 2 and 5, to get

5 = 2 x 2 + 1

Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 5 and 107 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(107,5) .

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Frequently Asked Questions on HCF of 610, 225, 107 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 610, 225, 107?

Answer: HCF of 610, 225, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 610, 225, 107 using Euclid's Algorithm?

Answer: For arbitrary numbers 610, 225, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.