Highest Common Factor of 721, 505 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, 505 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 505 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, 505 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, 505 is 1.
HCF(721, 505) = 1
HCF of 721, 505 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, 505 is 1.
Highest Common Factor of 721,505 is 1
Step 1: Since 721 > 505, we apply the division lemma to 721 and 505, to get
721 = 505 x 1 + 216
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 216 and 505, to get
505 = 216 x 2 + 73
Step 3: We consider the new divisor 216 and the new remainder 73, and apply the division lemma to get
216 = 73 x 2 + 70
We consider the new divisor 73 and the new remainder 70,and apply the division lemma to get
73 = 70 x 1 + 3
We consider the new divisor 70 and the new remainder 3,and apply the division lemma to get
70 = 3 x 23 + 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 721 and 505 is 1
Notice that 1 = HCF(3,1) = HCF(70,3) = HCF(73,70) = HCF(216,73) = HCF(505,216) = HCF(721,505) .
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Frequently Asked Questions on HCF of 721, 505 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, 505?
Answer: HCF of 721, 505 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 505 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 505 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.