Highest Common Factor of 5586, 8718 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 5586, 8718 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 5586, 8718 is 6 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 5586, 8718 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 5586, 8718 is 6.
HCF(5586, 8718) = 6
HCF of 5586, 8718 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5586, 8718 is 6.
Highest Common Factor of 5586,8718 is 6
Step 1: Since 8718 > 5586, we apply the division lemma to 8718 and 5586, to get
8718 = 5586 x 1 + 3132
Step 2: Since the reminder 5586 ≠ 0, we apply division lemma to 3132 and 5586, to get
5586 = 3132 x 1 + 2454
Step 3: We consider the new divisor 3132 and the new remainder 2454, and apply the division lemma to get
3132 = 2454 x 1 + 678
We consider the new divisor 2454 and the new remainder 678,and apply the division lemma to get
2454 = 678 x 3 + 420
We consider the new divisor 678 and the new remainder 420,and apply the division lemma to get
678 = 420 x 1 + 258
We consider the new divisor 420 and the new remainder 258,and apply the division lemma to get
420 = 258 x 1 + 162
We consider the new divisor 258 and the new remainder 162,and apply the division lemma to get
258 = 162 x 1 + 96
We consider the new divisor 162 and the new remainder 96,and apply the division lemma to get
162 = 96 x 1 + 66
We consider the new divisor 96 and the new remainder 66,and apply the division lemma to get
96 = 66 x 1 + 30
We consider the new divisor 66 and the new remainder 30,and apply the division lemma to get
66 = 30 x 2 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 5586 and 8718 is 6
Notice that 6 = HCF(30,6) = HCF(66,30) = HCF(96,66) = HCF(162,96) = HCF(258,162) = HCF(420,258) = HCF(678,420) = HCF(2454,678) = HCF(3132,2454) = HCF(5586,3132) = HCF(8718,5586) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 5586, 8718 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 5586, 8718?
Answer: HCF of 5586, 8718 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5586, 8718 using Euclid's Algorithm?
Answer: For arbitrary numbers 5586, 8718 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.