Highest Common Factor of 735, 1249, 4640 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 735, 1249, 4640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 735, 1249, 4640 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 735, 1249, 4640 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 735, 1249, 4640 is 1.

HCF(735, 1249, 4640) = 1

HCF of 735, 1249, 4640 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 735, 1249, 4640 is 1.

Highest Common Factor of 735,1249,4640 using Euclid's algorithm

Highest Common Factor of 735,1249,4640 is 1

Step 1: Since 1249 > 735, we apply the division lemma to 1249 and 735, to get

1249 = 735 x 1 + 514

Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 514 and 735, to get

735 = 514 x 1 + 221

Step 3: We consider the new divisor 514 and the new remainder 221, and apply the division lemma to get

514 = 221 x 2 + 72

We consider the new divisor 221 and the new remainder 72,and apply the division lemma to get

221 = 72 x 3 + 5

We consider the new divisor 72 and the new remainder 5,and apply the division lemma to get

72 = 5 x 14 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 735 and 1249 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(72,5) = HCF(221,72) = HCF(514,221) = HCF(735,514) = HCF(1249,735) .

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

Step 1: Since 4640 > 1, we apply the division lemma to 4640 and 1, to get

4640 = 1 x 4640 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4640 is 1

Notice that 1 = HCF(4640,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 735, 1249, 4640 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 735, 1249, 4640?

Answer: HCF of 735, 1249, 4640 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 735, 1249, 4640 using Euclid's Algorithm?

Answer: For arbitrary numbers 735, 1249, 4640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.