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 413, 715 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 715 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 413, 715 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 413, 715 is 1.
HCF(413, 715) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 413, 715 is 1.
Step 1: Since 715 > 413, we apply the division lemma to 715 and 413, to get
715 = 413 x 1 + 302
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 302 and 413, to get
413 = 302 x 1 + 111
Step 3: We consider the new divisor 302 and the new remainder 111, and apply the division lemma to get
302 = 111 x 2 + 80
We consider the new divisor 111 and the new remainder 80,and apply the division lemma to get
111 = 80 x 1 + 31
We consider the new divisor 80 and the new remainder 31,and apply the division lemma to get
80 = 31 x 2 + 18
We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get
31 = 18 x 1 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 413 and 715 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(80,31) = HCF(111,80) = HCF(302,111) = HCF(413,302) = HCF(715,413) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 413, 715?
Answer: HCF of 413, 715 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 715 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 715 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.