Highest Common Factor of 722, 8587 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 722, 8587 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 8587 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 722, 8587 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 722, 8587 is 1.
HCF(722, 8587) = 1
HCF of 722, 8587 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 8587 is 1.
Highest Common Factor of 722,8587 is 1
Step 1: Since 8587 > 722, we apply the division lemma to 8587 and 722, to get
8587 = 722 x 11 + 645
Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 645 and 722, to get
722 = 645 x 1 + 77
Step 3: We consider the new divisor 645 and the new remainder 77, and apply the division lemma to get
645 = 77 x 8 + 29
We consider the new divisor 77 and the new remainder 29,and apply the division lemma to get
77 = 29 x 2 + 19
We consider the new divisor 29 and the new remainder 19,and apply the division lemma to get
29 = 19 x 1 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 722 and 8587 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(29,19) = HCF(77,29) = HCF(645,77) = HCF(722,645) = HCF(8587,722) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 722, 8587 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 722, 8587?
Answer: HCF of 722, 8587 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 8587 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 8587 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.