Highest Common Factor of 558, 9687 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 558, 9687 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 558, 9687 is 3 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 558, 9687 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 558, 9687 is 3.
HCF(558, 9687) = 3
HCF of 558, 9687 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 558, 9687 is 3.
Highest Common Factor of 558,9687 is 3
Step 1: Since 9687 > 558, we apply the division lemma to 9687 and 558, to get
9687 = 558 x 17 + 201
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 201 and 558, to get
558 = 201 x 2 + 156
Step 3: We consider the new divisor 201 and the new remainder 156, and apply the division lemma to get
201 = 156 x 1 + 45
We consider the new divisor 156 and the new remainder 45,and apply the division lemma to get
156 = 45 x 3 + 21
We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get
45 = 21 x 2 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 558 and 9687 is 3
Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(156,45) = HCF(201,156) = HCF(558,201) = HCF(9687,558) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 558, 9687 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 558, 9687?
Answer: HCF of 558, 9687 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 558, 9687 using Euclid's Algorithm?
Answer: For arbitrary numbers 558, 9687 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.