Highest Common Factor of 413, 977 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 413, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 977 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, 977 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, 977 is 1.
HCF(413, 977) = 1
HCF of 413, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 413, 977 is 1.
Highest Common Factor of 413,977 is 1
Step 1: Since 977 > 413, we apply the division lemma to 977 and 413, to get
977 = 413 x 2 + 151
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 151 and 413, to get
413 = 151 x 2 + 111
Step 3: We consider the new divisor 151 and the new remainder 111, and apply the division lemma to get
151 = 111 x 1 + 40
We consider the new divisor 111 and the new remainder 40,and apply the division lemma to get
111 = 40 x 2 + 31
We consider the new divisor 40 and the new remainder 31,and apply the division lemma to get
40 = 31 x 1 + 9
We consider the new divisor 31 and the new remainder 9,and apply the division lemma to get
31 = 9 x 3 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 413 and 977 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(31,9) = HCF(40,31) = HCF(111,40) = HCF(151,111) = HCF(413,151) = HCF(977,413) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 413, 977 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 413, 977?
Answer: HCF of 413, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.