Highest Common Factor of 60, 13, 75 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 60, 13, 75 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 60, 13, 75 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 60, 13, 75 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 60, 13, 75 is 1.

HCF(60, 13, 75) = 1

HCF of 60, 13, 75 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 60, 13, 75 is 1.

Highest Common Factor of 60,13,75 using Euclid's algorithm

Highest Common Factor of 60,13,75 is 1

Step 1: Since 60 > 13, we apply the division lemma to 60 and 13, to get

60 = 13 x 4 + 8

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get

13 = 8 x 1 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 3

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

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

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 60 and 13 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(60,13) .

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

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

75 = 1 x 75 + 0

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

Notice that 1 = HCF(75,1) .

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Frequently Asked Questions on HCF of 60, 13, 75 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 60, 13, 75?

Answer: HCF of 60, 13, 75 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 60, 13, 75 using Euclid's Algorithm?

Answer: For arbitrary numbers 60, 13, 75 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.