Highest Common Factor of 74, 717, 125 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 74, 717, 125 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 74, 717, 125 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 74, 717, 125 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 74, 717, 125 is 1.

HCF(74, 717, 125) = 1

HCF of 74, 717, 125 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 74, 717, 125 is 1.

Highest Common Factor of 74,717,125 using Euclid's algorithm

Highest Common Factor of 74,717,125 is 1

Step 1: Since 717 > 74, we apply the division lemma to 717 and 74, to get

717 = 74 x 9 + 51

Step 2: Since the reminder 74 ≠ 0, we apply division lemma to 51 and 74, to get

74 = 51 x 1 + 23

Step 3: We consider the new divisor 51 and the new remainder 23, and apply the division lemma to get

51 = 23 x 2 + 5

We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get

23 = 5 x 4 + 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 74 and 717 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(51,23) = HCF(74,51) = HCF(717,74) .

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

Step 1: Since 125 > 1, we apply the division lemma to 125 and 1, to get

125 = 1 x 125 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 125 is 1

Notice that 1 = HCF(125,1) .

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Frequently Asked Questions on HCF of 74, 717, 125 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 74, 717, 125?

Answer: HCF of 74, 717, 125 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 74, 717, 125 using Euclid's Algorithm?

Answer: For arbitrary numbers 74, 717, 125 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.