Highest Common Factor of 575, 610, 602 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 575, 610, 602 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 575, 610, 602 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 575, 610, 602 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 575, 610, 602 is 1.

HCF(575, 610, 602) = 1

HCF of 575, 610, 602 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 575, 610, 602 is 1.

Highest Common Factor of 575,610,602 using Euclid's algorithm

Highest Common Factor of 575,610,602 is 1

Step 1: Since 610 > 575, we apply the division lemma to 610 and 575, to get

610 = 575 x 1 + 35

Step 2: Since the reminder 575 ≠ 0, we apply division lemma to 35 and 575, to get

575 = 35 x 16 + 15

Step 3: We consider the new divisor 35 and the new remainder 15, and apply the division lemma to get

35 = 15 x 2 + 5

We consider the new divisor 15 and the new remainder 5, and apply the division lemma to get

15 = 5 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 575 and 610 is 5

Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(575,35) = HCF(610,575) .

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

Step 1: Since 602 > 5, we apply the division lemma to 602 and 5, to get

602 = 5 x 120 + 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 602 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(602,5) .

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Frequently Asked Questions on HCF of 575, 610, 602 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 575, 610, 602?

Answer: HCF of 575, 610, 602 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 575, 610, 602 using Euclid's Algorithm?

Answer: For arbitrary numbers 575, 610, 602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.