Highest Common Factor of 412, 2286, 9688 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 412, 2286, 9688 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 412, 2286, 9688 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 412, 2286, 9688 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 412, 2286, 9688 is 2.
HCF(412, 2286, 9688) = 2
HCF of 412, 2286, 9688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 412, 2286, 9688 is 2.
Highest Common Factor of 412,2286,9688 is 2
Step 1: Since 2286 > 412, we apply the division lemma to 2286 and 412, to get
2286 = 412 x 5 + 226
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 226 and 412, to get
412 = 226 x 1 + 186
Step 3: We consider the new divisor 226 and the new remainder 186, and apply the division lemma to get
226 = 186 x 1 + 40
We consider the new divisor 186 and the new remainder 40,and apply the division lemma to get
186 = 40 x 4 + 26
We consider the new divisor 40 and the new remainder 26,and apply the division lemma to get
40 = 26 x 1 + 14
We consider the new divisor 26 and the new remainder 14,and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 412 and 2286 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(186,40) = HCF(226,186) = HCF(412,226) = HCF(2286,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9688 > 2, we apply the division lemma to 9688 and 2, to get
9688 = 2 x 4844 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9688 is 2
Notice that 2 = HCF(9688,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 412, 2286, 9688 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 412, 2286, 9688?
Answer: HCF of 412, 2286, 9688 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 412, 2286, 9688 using Euclid's Algorithm?
Answer: For arbitrary numbers 412, 2286, 9688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.