Highest Common Factor of 1627, 1340, 15644 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 1627, 1340, 15644 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1627, 1340, 15644 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 1627, 1340, 15644 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 1627, 1340, 15644 is 1.

HCF(1627, 1340, 15644) = 1

HCF of 1627, 1340, 15644 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 1627, 1340, 15644 is 1.

Highest Common Factor of 1627,1340,15644 using Euclid's algorithm

Highest Common Factor of 1627,1340,15644 is 1

Step 1: Since 1627 > 1340, we apply the division lemma to 1627 and 1340, to get

1627 = 1340 x 1 + 287

Step 2: Since the reminder 1340 ≠ 0, we apply division lemma to 287 and 1340, to get

1340 = 287 x 4 + 192

Step 3: We consider the new divisor 287 and the new remainder 192, and apply the division lemma to get

287 = 192 x 1 + 95

We consider the new divisor 192 and the new remainder 95,and apply the division lemma to get

192 = 95 x 2 + 2

We consider the new divisor 95 and the new remainder 2,and apply the division lemma to get

95 = 2 x 47 + 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 1627 and 1340 is 1

Notice that 1 = HCF(2,1) = HCF(95,2) = HCF(192,95) = HCF(287,192) = HCF(1340,287) = HCF(1627,1340) .

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

Step 1: Since 15644 > 1, we apply the division lemma to 15644 and 1, to get

15644 = 1 x 15644 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15644 is 1

Notice that 1 = HCF(15644,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 1627, 1340, 15644 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 1627, 1340, 15644?

Answer: HCF of 1627, 1340, 15644 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1627, 1340, 15644 using Euclid's Algorithm?

Answer: For arbitrary numbers 1627, 1340, 15644 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.