Highest Common Factor of 7505, 8270, 77876 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 7505, 8270, 77876 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7505, 8270, 77876 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 7505, 8270, 77876 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 7505, 8270, 77876 is 1.

HCF(7505, 8270, 77876) = 1

HCF of 7505, 8270, 77876 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 7505, 8270, 77876 is 1.

Highest Common Factor of 7505,8270,77876 using Euclid's algorithm

Highest Common Factor of 7505,8270,77876 is 1

Step 1: Since 8270 > 7505, we apply the division lemma to 8270 and 7505, to get

8270 = 7505 x 1 + 765

Step 2: Since the reminder 7505 ≠ 0, we apply division lemma to 765 and 7505, to get

7505 = 765 x 9 + 620

Step 3: We consider the new divisor 765 and the new remainder 620, and apply the division lemma to get

765 = 620 x 1 + 145

We consider the new divisor 620 and the new remainder 145,and apply the division lemma to get

620 = 145 x 4 + 40

We consider the new divisor 145 and the new remainder 40,and apply the division lemma to get

145 = 40 x 3 + 25

We consider the new divisor 40 and the new remainder 25,and apply the division lemma to get

40 = 25 x 1 + 15

We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get

25 = 15 x 1 + 10

We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get

15 = 10 x 1 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 7505 and 8270 is 5

Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(145,40) = HCF(620,145) = HCF(765,620) = HCF(7505,765) = HCF(8270,7505) .

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

Step 1: Since 77876 > 5, we apply the division lemma to 77876 and 5, to get

77876 = 5 x 15575 + 1

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 77876 is 1

Notice that 1 = HCF(5,1) = HCF(77876,5) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 7505, 8270, 77876 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 7505, 8270, 77876?

Answer: HCF of 7505, 8270, 77876 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7505, 8270, 77876 using Euclid's Algorithm?

Answer: For arbitrary numbers 7505, 8270, 77876 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.