Highest Common Factor of 9709, 5096, 34148 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 9709, 5096, 34148 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9709, 5096, 34148 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 9709, 5096, 34148 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 9709, 5096, 34148 is 1.
HCF(9709, 5096, 34148) = 1
HCF of 9709, 5096, 34148 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9709, 5096, 34148 is 1.
Highest Common Factor of 9709,5096,34148 is 1
Step 1: Since 9709 > 5096, we apply the division lemma to 9709 and 5096, to get
9709 = 5096 x 1 + 4613
Step 2: Since the reminder 5096 ≠ 0, we apply division lemma to 4613 and 5096, to get
5096 = 4613 x 1 + 483
Step 3: We consider the new divisor 4613 and the new remainder 483, and apply the division lemma to get
4613 = 483 x 9 + 266
We consider the new divisor 483 and the new remainder 266,and apply the division lemma to get
483 = 266 x 1 + 217
We consider the new divisor 266 and the new remainder 217,and apply the division lemma to get
266 = 217 x 1 + 49
We consider the new divisor 217 and the new remainder 49,and apply the division lemma to get
217 = 49 x 4 + 21
We consider the new divisor 49 and the new remainder 21,and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 9709 and 5096 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(217,49) = HCF(266,217) = HCF(483,266) = HCF(4613,483) = HCF(5096,4613) = HCF(9709,5096) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 34148 > 7, we apply the division lemma to 34148 and 7, to get
34148 = 7 x 4878 + 2
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 2 and 7, to get
7 = 2 x 3 + 1
Step 3: 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 7 and 34148 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(34148,7) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9709, 5096, 34148 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 9709, 5096, 34148?
Answer: HCF of 9709, 5096, 34148 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9709, 5096, 34148 using Euclid's Algorithm?
Answer: For arbitrary numbers 9709, 5096, 34148 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.