Highest Common Factor of 8116, 640 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 8116, 640 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 8116, 640 is 4 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 8116, 640 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 8116, 640 is 4.
HCF(8116, 640) = 4
HCF of 8116, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8116, 640 is 4.
Highest Common Factor of 8116,640 is 4
Step 1: Since 8116 > 640, we apply the division lemma to 8116 and 640, to get
8116 = 640 x 12 + 436
Step 2: Since the reminder 640 ≠ 0, we apply division lemma to 436 and 640, to get
640 = 436 x 1 + 204
Step 3: We consider the new divisor 436 and the new remainder 204, and apply the division lemma to get
436 = 204 x 2 + 28
We consider the new divisor 204 and the new remainder 28,and apply the division lemma to get
204 = 28 x 7 + 8
We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get
28 = 8 x 3 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 8116 and 640 is 4
Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(204,28) = HCF(436,204) = HCF(640,436) = HCF(8116,640) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8116, 640 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 8116, 640?
Answer: HCF of 8116, 640 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8116, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 8116, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.