Highest Common Factor of 655, 1920, 7028 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 655, 1920, 7028 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 655, 1920, 7028 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 655, 1920, 7028 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 655, 1920, 7028 is 1.

HCF(655, 1920, 7028) = 1

HCF of 655, 1920, 7028 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 655, 1920, 7028 is 1.

Highest Common Factor of 655,1920,7028 using Euclid's algorithm

Highest Common Factor of 655,1920,7028 is 1

Step 1: Since 1920 > 655, we apply the division lemma to 1920 and 655, to get

1920 = 655 x 2 + 610

Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 610 and 655, to get

655 = 610 x 1 + 45

Step 3: We consider the new divisor 610 and the new remainder 45, and apply the division lemma to get

610 = 45 x 13 + 25

We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get

45 = 25 x 1 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 655 and 1920 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(610,45) = HCF(655,610) = HCF(1920,655) .

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

Step 1: Since 7028 > 5, we apply the division lemma to 7028 and 5, to get

7028 = 5 x 1405 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 5 and 7028 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(7028,5) .

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Frequently Asked Questions on HCF of 655, 1920, 7028 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 655, 1920, 7028?

Answer: HCF of 655, 1920, 7028 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 655, 1920, 7028 using Euclid's Algorithm?

Answer: For arbitrary numbers 655, 1920, 7028 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.