Highest Common Factor of 60, 760, 723 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, 760, 723 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 60, 760, 723 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, 760, 723 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, 760, 723 is 1.

HCF(60, 760, 723) = 1

HCF of 60, 760, 723 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, 760, 723 is 1.

Highest Common Factor of 60,760,723 using Euclid's algorithm

Highest Common Factor of 60,760,723 is 1

Step 1: Since 760 > 60, we apply the division lemma to 760 and 60, to get

760 = 60 x 12 + 40

Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 40 and 60, to get

60 = 40 x 1 + 20

Step 3: We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get

40 = 20 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 60 and 760 is 20

Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(760,60) .

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

Step 1: Since 723 > 20, we apply the division lemma to 723 and 20, to get

723 = 20 x 36 + 3

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 3 and 20, to get

20 = 3 x 6 + 2

Step 3: 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 20 and 723 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(723,20) .

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Frequently Asked Questions on HCF of 60, 760, 723 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, 760, 723?

Answer: HCF of 60, 760, 723 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 60, 760, 723 using Euclid's Algorithm?

Answer: For arbitrary numbers 60, 760, 723 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.