Highest Common Factor of 675, 125, 580, 751 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 675, 125, 580, 751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 675, 125, 580, 751 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 675, 125, 580, 751 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 675, 125, 580, 751 is 1.

HCF(675, 125, 580, 751) = 1

HCF of 675, 125, 580, 751 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 675, 125, 580, 751 is 1.

Highest Common Factor of 675,125,580,751 using Euclid's algorithm

Highest Common Factor of 675,125,580,751 is 1

Step 1: Since 675 > 125, we apply the division lemma to 675 and 125, to get

675 = 125 x 5 + 50

Step 2: Since the reminder 125 ≠ 0, we apply division lemma to 50 and 125, to get

125 = 50 x 2 + 25

Step 3: We consider the new divisor 50 and the new remainder 25, and apply the division lemma to get

50 = 25 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 25, the HCF of 675 and 125 is 25

Notice that 25 = HCF(50,25) = HCF(125,50) = HCF(675,125) .

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

Step 1: Since 580 > 25, we apply the division lemma to 580 and 25, to get

580 = 25 x 23 + 5

Step 2: Since the reminder 25 ≠ 0, we apply division lemma to 5 and 25, to get

25 = 5 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 25 and 580 is 5

Notice that 5 = HCF(25,5) = HCF(580,25) .

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

Step 1: Since 751 > 5, we apply the division lemma to 751 and 5, to get

751 = 5 x 150 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 751 is 1

Notice that 1 = HCF(5,1) = HCF(751,5) .

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Frequently Asked Questions on HCF of 675, 125, 580, 751 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 675, 125, 580, 751?

Answer: HCF of 675, 125, 580, 751 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 675, 125, 580, 751 using Euclid's Algorithm?

Answer: For arbitrary numbers 675, 125, 580, 751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.