Highest Common Factor of 615, 708, 800, 280 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 615, 708, 800, 280 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 615, 708, 800, 280 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 615, 708, 800, 280 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 615, 708, 800, 280 is 1.

HCF(615, 708, 800, 280) = 1

HCF of 615, 708, 800, 280 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 615, 708, 800, 280 is 1.

Highest Common Factor of 615,708,800,280 using Euclid's algorithm

Highest Common Factor of 615,708,800,280 is 1

Step 1: Since 708 > 615, we apply the division lemma to 708 and 615, to get

708 = 615 x 1 + 93

Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 93 and 615, to get

615 = 93 x 6 + 57

Step 3: We consider the new divisor 93 and the new remainder 57, and apply the division lemma to get

93 = 57 x 1 + 36

We consider the new divisor 57 and the new remainder 36,and apply the division lemma to get

57 = 36 x 1 + 21

We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get

36 = 21 x 1 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 615 and 708 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(93,57) = HCF(615,93) = HCF(708,615) .

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

Step 1: Since 800 > 3, we apply the division lemma to 800 and 3, to get

800 = 3 x 266 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 800 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(800,3) .

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

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

280 = 1 x 280 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 280 is 1

Notice that 1 = HCF(280,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 615, 708, 800, 280 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 615, 708, 800, 280?

Answer: HCF of 615, 708, 800, 280 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 615, 708, 800, 280 using Euclid's Algorithm?

Answer: For arbitrary numbers 615, 708, 800, 280 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.