Highest Common Factor of 280, 734, 657 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 280, 734, 657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 280, 734, 657 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 280, 734, 657 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 280, 734, 657 is 1.

HCF(280, 734, 657) = 1

HCF of 280, 734, 657 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 280, 734, 657 is 1.

Highest Common Factor of 280,734,657 using Euclid's algorithm

Highest Common Factor of 280,734,657 is 1

Step 1: Since 734 > 280, we apply the division lemma to 734 and 280, to get

734 = 280 x 2 + 174

Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 174 and 280, to get

280 = 174 x 1 + 106

Step 3: We consider the new divisor 174 and the new remainder 106, and apply the division lemma to get

174 = 106 x 1 + 68

We consider the new divisor 106 and the new remainder 68,and apply the division lemma to get

106 = 68 x 1 + 38

We consider the new divisor 68 and the new remainder 38,and apply the division lemma to get

68 = 38 x 1 + 30

We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get

38 = 30 x 1 + 8

We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get

30 = 8 x 3 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 280 and 734 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(68,38) = HCF(106,68) = HCF(174,106) = HCF(280,174) = HCF(734,280) .

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

Step 1: Since 657 > 2, we apply the division lemma to 657 and 2, to get

657 = 2 x 328 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 657 is 1

Notice that 1 = HCF(2,1) = HCF(657,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 280, 734, 657 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 280, 734, 657?

Answer: HCF of 280, 734, 657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 280, 734, 657 using Euclid's Algorithm?

Answer: For arbitrary numbers 280, 734, 657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.