Highest Common Factor of 721, 515, 61 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, 515, 61 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 515, 61 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, 515, 61 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, 515, 61 is 1.
HCF(721, 515, 61) = 1
HCF of 721, 515, 61 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, 515, 61 is 1.
Highest Common Factor of 721,515,61 is 1
Step 1: Since 721 > 515, we apply the division lemma to 721 and 515, to get
721 = 515 x 1 + 206
Step 2: Since the reminder 515 ≠ 0, we apply division lemma to 206 and 515, to get
515 = 206 x 2 + 103
Step 3: We consider the new divisor 206 and the new remainder 103, and apply the division lemma to get
206 = 103 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 103, the HCF of 721 and 515 is 103
Notice that 103 = HCF(206,103) = HCF(515,206) = HCF(721,515) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 103 > 61, we apply the division lemma to 103 and 61, to get
103 = 61 x 1 + 42
Step 2: Since the reminder 61 ≠ 0, we apply division lemma to 42 and 61, to get
61 = 42 x 1 + 19
Step 3: We consider the new divisor 42 and the new remainder 19, and apply the division lemma to get
42 = 19 x 2 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 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 103 and 61 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(42,19) = HCF(61,42) = HCF(103,61) .
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Frequently Asked Questions on HCF of 721, 515, 61 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, 515, 61?
Answer: HCF of 721, 515, 61 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 515, 61 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 515, 61 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.