Highest Common Factor of 61, 75, 600 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 61, 75, 600 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 61, 75, 600 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 61, 75, 600 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 61, 75, 600 is 1.

HCF(61, 75, 600) = 1

HCF of 61, 75, 600 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 61, 75, 600 is 1.

Highest Common Factor of 61,75,600 using Euclid's algorithm

Highest Common Factor of 61,75,600 is 1

Step 1: Since 75 > 61, we apply the division lemma to 75 and 61, to get

75 = 61 x 1 + 14

Step 2: Since the reminder 61 ≠ 0, we apply division lemma to 14 and 61, to get

61 = 14 x 4 + 5

Step 3: We consider the new divisor 14 and the new remainder 5, and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 61 and 75 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(61,14) = HCF(75,61) .

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

Step 1: Since 600 > 1, we apply the division lemma to 600 and 1, to get

600 = 1 x 600 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 600 is 1

Notice that 1 = HCF(600,1) .

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Frequently Asked Questions on HCF of 61, 75, 600 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 61, 75, 600?

Answer: HCF of 61, 75, 600 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 61, 75, 600 using Euclid's Algorithm?

Answer: For arbitrary numbers 61, 75, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.