Highest Common Factor of 652, 778, 720 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 652, 778, 720 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 652, 778, 720 is 2 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 652, 778, 720 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 652, 778, 720 is 2.

HCF(652, 778, 720) = 2

HCF of 652, 778, 720 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 652, 778, 720 is 2.

Highest Common Factor of 652,778,720 using Euclid's algorithm

Highest Common Factor of 652,778,720 is 2

Step 1: Since 778 > 652, we apply the division lemma to 778 and 652, to get

778 = 652 x 1 + 126

Step 2: Since the reminder 652 ≠ 0, we apply division lemma to 126 and 652, to get

652 = 126 x 5 + 22

Step 3: We consider the new divisor 126 and the new remainder 22, and apply the division lemma to get

126 = 22 x 5 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 652 and 778 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(126,22) = HCF(652,126) = HCF(778,652) .

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

Step 1: Since 720 > 2, we apply the division lemma to 720 and 2, to get

720 = 2 x 360 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 720 is 2

Notice that 2 = HCF(720,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 652, 778, 720 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 652, 778, 720?

Answer: HCF of 652, 778, 720 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 652, 778, 720 using Euclid's Algorithm?

Answer: For arbitrary numbers 652, 778, 720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.