Highest Common Factor of 687, 374, 525 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 687, 374, 525 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 687, 374, 525 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 687, 374, 525 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 687, 374, 525 is 1.

HCF(687, 374, 525) = 1

HCF of 687, 374, 525 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 687, 374, 525 is 1.

Highest Common Factor of 687,374,525 using Euclid's algorithm

Highest Common Factor of 687,374,525 is 1

Step 1: Since 687 > 374, we apply the division lemma to 687 and 374, to get

687 = 374 x 1 + 313

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 313 and 374, to get

374 = 313 x 1 + 61

Step 3: We consider the new divisor 313 and the new remainder 61, and apply the division lemma to get

313 = 61 x 5 + 8

We consider the new divisor 61 and the new remainder 8,and apply the division lemma to get

61 = 8 x 7 + 5

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 687 and 374 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(61,8) = HCF(313,61) = HCF(374,313) = HCF(687,374) .

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

Step 1: Since 525 > 1, we apply the division lemma to 525 and 1, to get

525 = 1 x 525 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 525 is 1

Notice that 1 = HCF(525,1) .

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Frequently Asked Questions on HCF of 687, 374, 525 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 687, 374, 525?

Answer: HCF of 687, 374, 525 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 687, 374, 525 using Euclid's Algorithm?

Answer: For arbitrary numbers 687, 374, 525 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.