Highest Common Factor of 374, 631, 87 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 374, 631, 87 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 374, 631, 87 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 374, 631, 87 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 374, 631, 87 is 1.

HCF(374, 631, 87) = 1

HCF of 374, 631, 87 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 374, 631, 87 is 1.

Highest Common Factor of 374,631,87 using Euclid's algorithm

Highest Common Factor of 374,631,87 is 1

Step 1: Since 631 > 374, we apply the division lemma to 631 and 374, to get

631 = 374 x 1 + 257

Step 2: Since the reminder 374 ≠ 0, we apply division lemma to 257 and 374, to get

374 = 257 x 1 + 117

Step 3: We consider the new divisor 257 and the new remainder 117, and apply the division lemma to get

257 = 117 x 2 + 23

We consider the new divisor 117 and the new remainder 23,and apply the division lemma to get

117 = 23 x 5 + 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 374 and 631 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(117,23) = HCF(257,117) = HCF(374,257) = HCF(631,374) .

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

Step 1: Since 87 > 1, we apply the division lemma to 87 and 1, to get

87 = 1 x 87 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 87 is 1

Notice that 1 = HCF(87,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 374, 631, 87 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 374, 631, 87?

Answer: HCF of 374, 631, 87 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 374, 631, 87 using Euclid's Algorithm?

Answer: For arbitrary numbers 374, 631, 87 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.