Highest Common Factor of 721, 205 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 721, 205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 205 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 721, 205 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 721, 205 is 1.
HCF(721, 205) = 1
HCF of 721, 205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 205 is 1.
Highest Common Factor of 721,205 is 1
Step 1: Since 721 > 205, we apply the division lemma to 721 and 205, to get
721 = 205 x 3 + 106
Step 2: Since the reminder 205 ≠ 0, we apply division lemma to 106 and 205, to get
205 = 106 x 1 + 99
Step 3: We consider the new divisor 106 and the new remainder 99, and apply the division lemma to get
106 = 99 x 1 + 7
We consider the new divisor 99 and the new remainder 7,and apply the division lemma to get
99 = 7 x 14 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 721 and 205 is 1
Notice that 1 = HCF(7,1) = HCF(99,7) = HCF(106,99) = HCF(205,106) = HCF(721,205) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 721, 205 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 721, 205?
Answer: HCF of 721, 205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 205 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
