Highest Common Factor of 431, 4922, 4096 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 431, 4922, 4096 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 431, 4922, 4096 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 431, 4922, 4096 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 431, 4922, 4096 is 1.
HCF(431, 4922, 4096) = 1
HCF of 431, 4922, 4096 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 431, 4922, 4096 is 1.
Highest Common Factor of 431,4922,4096 is 1
Step 1: Since 4922 > 431, we apply the division lemma to 4922 and 431, to get
4922 = 431 x 11 + 181
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 181 and 431, to get
431 = 181 x 2 + 69
Step 3: We consider the new divisor 181 and the new remainder 69, and apply the division lemma to get
181 = 69 x 2 + 43
We consider the new divisor 69 and the new remainder 43,and apply the division lemma to get
69 = 43 x 1 + 26
We consider the new divisor 43 and the new remainder 26,and apply the division lemma to get
43 = 26 x 1 + 17
We consider the new divisor 26 and the new remainder 17,and apply the division lemma to get
26 = 17 x 1 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 431 and 4922 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(43,26) = HCF(69,43) = HCF(181,69) = HCF(431,181) = HCF(4922,431) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4096 > 1, we apply the division lemma to 4096 and 1, to get
4096 = 1 x 4096 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4096 is 1
Notice that 1 = HCF(4096,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 431, 4922, 4096 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 431, 4922, 4096?
Answer: HCF of 431, 4922, 4096 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 431, 4922, 4096 using Euclid's Algorithm?
Answer: For arbitrary numbers 431, 4922, 4096 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
