Highest Common Factor of 987, 274, 948 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, 274, 948 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 987, 274, 948 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, 274, 948 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, 274, 948 is 1.

HCF(987, 274, 948) = 1

HCF of 987, 274, 948 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, 274, 948 is 1.

Highest Common Factor of 987,274,948 using Euclid's algorithm

Highest Common Factor of 987,274,948 is 1

Step 1: Since 987 > 274, we apply the division lemma to 987 and 274, to get

987 = 274 x 3 + 165

Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 165 and 274, to get

274 = 165 x 1 + 109

Step 3: We consider the new divisor 165 and the new remainder 109, and apply the division lemma to get

165 = 109 x 1 + 56

We consider the new divisor 109 and the new remainder 56,and apply the division lemma to get

109 = 56 x 1 + 53

We consider the new divisor 56 and the new remainder 53,and apply the division lemma to get

56 = 53 x 1 + 3

We consider the new divisor 53 and the new remainder 3,and apply the division lemma to get

53 = 3 x 17 + 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 987 and 274 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(53,3) = HCF(56,53) = HCF(109,56) = HCF(165,109) = HCF(274,165) = HCF(987,274) .

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

Step 1: Since 948 > 1, we apply the division lemma to 948 and 1, to get

948 = 1 x 948 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 948 is 1

Notice that 1 = HCF(948,1) .

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Frequently Asked Questions on HCF of 987, 274, 948 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, 274, 948?

Answer: HCF of 987, 274, 948 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 987, 274, 948 using Euclid's Algorithm?

Answer: For arbitrary numbers 987, 274, 948 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.