Highest Common Factor of 443, 721 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 443, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 443, 721 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 443, 721 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 443, 721 is 1.
HCF(443, 721) = 1
HCF of 443, 721 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 443, 721 is 1.
Highest Common Factor of 443,721 is 1
Step 1: Since 721 > 443, we apply the division lemma to 721 and 443, to get
721 = 443 x 1 + 278
Step 2: Since the reminder 443 ≠ 0, we apply division lemma to 278 and 443, to get
443 = 278 x 1 + 165
Step 3: We consider the new divisor 278 and the new remainder 165, and apply the division lemma to get
278 = 165 x 1 + 113
We consider the new divisor 165 and the new remainder 113,and apply the division lemma to get
165 = 113 x 1 + 52
We consider the new divisor 113 and the new remainder 52,and apply the division lemma to get
113 = 52 x 2 + 9
We consider the new divisor 52 and the new remainder 9,and apply the division lemma to get
52 = 9 x 5 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 443 and 721 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(52,9) = HCF(113,52) = HCF(165,113) = HCF(278,165) = HCF(443,278) = HCF(721,443) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 443, 721 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 443, 721?
Answer: HCF of 443, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 443, 721 using Euclid's Algorithm?
Answer: For arbitrary numbers 443, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.