Highest Common Factor of 987, 674, 265 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 987, 674, 265 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 987, 674, 265 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 987, 674, 265 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 987, 674, 265 is 1.

HCF(987, 674, 265) = 1

HCF of 987, 674, 265 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 987, 674, 265 is 1.

Highest Common Factor of 987,674,265 using Euclid's algorithm

Highest Common Factor of 987,674,265 is 1

Step 1: Since 987 > 674, we apply the division lemma to 987 and 674, to get

987 = 674 x 1 + 313

Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 313 and 674, to get

674 = 313 x 2 + 48

Step 3: We consider the new divisor 313 and the new remainder 48, and apply the division lemma to get

313 = 48 x 6 + 25

We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get

48 = 25 x 1 + 23

We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get

25 = 23 x 1 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 987 and 674 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(313,48) = HCF(674,313) = HCF(987,674) .

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

Step 1: Since 265 > 1, we apply the division lemma to 265 and 1, to get

265 = 1 x 265 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 265 is 1

Notice that 1 = HCF(265,1) .

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Frequently Asked Questions on HCF of 987, 674, 265 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 987, 674, 265?

Answer: HCF of 987, 674, 265 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 987, 674, 265 using Euclid's Algorithm?

Answer: For arbitrary numbers 987, 674, 265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.