Highest Common Factor of 577, 6643 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 577, 6643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 577, 6643 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 577, 6643 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 577, 6643 is 1.
HCF(577, 6643) = 1
HCF of 577, 6643 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 577, 6643 is 1.
Highest Common Factor of 577,6643 is 1
Step 1: Since 6643 > 577, we apply the division lemma to 6643 and 577, to get
6643 = 577 x 11 + 296
Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 296 and 577, to get
577 = 296 x 1 + 281
Step 3: We consider the new divisor 296 and the new remainder 281, and apply the division lemma to get
296 = 281 x 1 + 15
We consider the new divisor 281 and the new remainder 15,and apply the division lemma to get
281 = 15 x 18 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 577 and 6643 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(281,15) = HCF(296,281) = HCF(577,296) = HCF(6643,577) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 577, 6643 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 577, 6643?
Answer: HCF of 577, 6643 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 577, 6643 using Euclid's Algorithm?
Answer: For arbitrary numbers 577, 6643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.