Highest Common Factor of 757, 274, 625 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 757, 274, 625 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 757, 274, 625 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 757, 274, 625 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 757, 274, 625 is 1.

HCF(757, 274, 625) = 1

HCF of 757, 274, 625 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 757, 274, 625 is 1.

Highest Common Factor of 757,274,625 using Euclid's algorithm

Highest Common Factor of 757,274,625 is 1

Step 1: Since 757 > 274, we apply the division lemma to 757 and 274, to get

757 = 274 x 2 + 209

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 209 and 274, to get

274 = 209 x 1 + 65

Step 3: We consider the new divisor 209 and the new remainder 65, and apply the division lemma to get

209 = 65 x 3 + 14

We consider the new divisor 65 and the new remainder 14,and apply the division lemma to get

65 = 14 x 4 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 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 757 and 274 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(65,14) = HCF(209,65) = HCF(274,209) = HCF(757,274) .

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

Step 1: Since 625 > 1, we apply the division lemma to 625 and 1, to get

625 = 1 x 625 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 625 is 1

Notice that 1 = HCF(625,1) .

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Frequently Asked Questions on HCF of 757, 274, 625 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 757, 274, 625?

Answer: HCF of 757, 274, 625 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 757, 274, 625 using Euclid's Algorithm?

Answer: For arbitrary numbers 757, 274, 625 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.