Highest Common Factor of 372, 561, 610 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 372, 561, 610 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 372, 561, 610 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 372, 561, 610 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 372, 561, 610 is 1.

HCF(372, 561, 610) = 1

HCF of 372, 561, 610 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 372, 561, 610 is 1.

Highest Common Factor of 372,561,610 using Euclid's algorithm

Highest Common Factor of 372,561,610 is 1

Step 1: Since 561 > 372, we apply the division lemma to 561 and 372, to get

561 = 372 x 1 + 189

Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 189 and 372, to get

372 = 189 x 1 + 183

Step 3: We consider the new divisor 189 and the new remainder 183, and apply the division lemma to get

189 = 183 x 1 + 6

We consider the new divisor 183 and the new remainder 6,and apply the division lemma to get

183 = 6 x 30 + 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 372 and 561 is 3

Notice that 3 = HCF(6,3) = HCF(183,6) = HCF(189,183) = HCF(372,189) = HCF(561,372) .

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

Step 1: Since 610 > 3, we apply the division lemma to 610 and 3, to get

610 = 3 x 203 + 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 610 is 1

Notice that 1 = HCF(3,1) = HCF(610,3) .

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Frequently Asked Questions on HCF of 372, 561, 610 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 372, 561, 610?

Answer: HCF of 372, 561, 610 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 372, 561, 610 using Euclid's Algorithm?

Answer: For arbitrary numbers 372, 561, 610 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.