Highest Common Factor of 460, 413 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 460, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 413 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 460, 413 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 460, 413 is 1.
HCF(460, 413) = 1
HCF of 460, 413 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 413 is 1.
Highest Common Factor of 460,413 is 1
Step 1: Since 460 > 413, we apply the division lemma to 460 and 413, to get
460 = 413 x 1 + 47
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 47 and 413, to get
413 = 47 x 8 + 37
Step 3: We consider the new divisor 47 and the new remainder 37, and apply the division lemma to get
47 = 37 x 1 + 10
We consider the new divisor 37 and the new remainder 10,and apply the division lemma to get
37 = 10 x 3 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 460 and 413 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(37,10) = HCF(47,37) = HCF(413,47) = HCF(460,413) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 460, 413 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 460, 413?
Answer: HCF of 460, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.