Highest Common Factor of 8578, 4877 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 8578, 4877 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8578, 4877 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 8578, 4877 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 8578, 4877 is 1.

HCF(8578, 4877) = 1

HCF of 8578, 4877 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 8578, 4877 is 1.

Highest Common Factor of 8578,4877 using Euclid's algorithm

Highest Common Factor of 8578,4877 is 1

Step 1: Since 8578 > 4877, we apply the division lemma to 8578 and 4877, to get

8578 = 4877 x 1 + 3701

Step 2: Since the reminder 4877 ≠ 0, we apply division lemma to 3701 and 4877, to get

4877 = 3701 x 1 + 1176

Step 3: We consider the new divisor 3701 and the new remainder 1176, and apply the division lemma to get

3701 = 1176 x 3 + 173

We consider the new divisor 1176 and the new remainder 173,and apply the division lemma to get

1176 = 173 x 6 + 138

We consider the new divisor 173 and the new remainder 138,and apply the division lemma to get

173 = 138 x 1 + 35

We consider the new divisor 138 and the new remainder 35,and apply the division lemma to get

138 = 35 x 3 + 33

We consider the new divisor 35 and the new remainder 33,and apply the division lemma to get

35 = 33 x 1 + 2

We consider the new divisor 33 and the new remainder 2,and apply the division lemma to get

33 = 2 x 16 + 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 8578 and 4877 is 1

Notice that 1 = HCF(2,1) = HCF(33,2) = HCF(35,33) = HCF(138,35) = HCF(173,138) = HCF(1176,173) = HCF(3701,1176) = HCF(4877,3701) = HCF(8578,4877) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 8578, 4877 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 8578, 4877?

Answer: HCF of 8578, 4877 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8578, 4877 using Euclid's Algorithm?

Answer: For arbitrary numbers 8578, 4877 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.