Highest Common Factor of 9698, 2168 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 9698, 2168 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9698, 2168 is 2 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 9698, 2168 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 9698, 2168 is 2.
HCF(9698, 2168) = 2
HCF of 9698, 2168 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9698, 2168 is 2.
Highest Common Factor of 9698,2168 is 2
Step 1: Since 9698 > 2168, we apply the division lemma to 9698 and 2168, to get
9698 = 2168 x 4 + 1026
Step 2: Since the reminder 2168 ≠ 0, we apply division lemma to 1026 and 2168, to get
2168 = 1026 x 2 + 116
Step 3: We consider the new divisor 1026 and the new remainder 116, and apply the division lemma to get
1026 = 116 x 8 + 98
We consider the new divisor 116 and the new remainder 98,and apply the division lemma to get
116 = 98 x 1 + 18
We consider the new divisor 98 and the new remainder 18,and apply the division lemma to get
98 = 18 x 5 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9698 and 2168 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(98,18) = HCF(116,98) = HCF(1026,116) = HCF(2168,1026) = HCF(9698,2168) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9698, 2168 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 9698, 2168?
Answer: HCF of 9698, 2168 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9698, 2168 using Euclid's Algorithm?
Answer: For arbitrary numbers 9698, 2168 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.