Highest Common Factor of 230, 1908, 9814 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 230, 1908, 9814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 230, 1908, 9814 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 230, 1908, 9814 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 230, 1908, 9814 is 2.
HCF(230, 1908, 9814) = 2
HCF of 230, 1908, 9814 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 230, 1908, 9814 is 2.
Highest Common Factor of 230,1908,9814 is 2
Step 1: Since 1908 > 230, we apply the division lemma to 1908 and 230, to get
1908 = 230 x 8 + 68
Step 2: Since the reminder 230 ≠ 0, we apply division lemma to 68 and 230, to get
230 = 68 x 3 + 26
Step 3: We consider the new divisor 68 and the new remainder 26, and apply the division lemma to get
68 = 26 x 2 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 230 and 1908 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(68,26) = HCF(230,68) = HCF(1908,230) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9814 > 2, we apply the division lemma to 9814 and 2, to get
9814 = 2 x 4907 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9814 is 2
Notice that 2 = HCF(9814,2) .
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Frequently Asked Questions on HCF of 230, 1908, 9814 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 230, 1908, 9814?
Answer: HCF of 230, 1908, 9814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 230, 1908, 9814 using Euclid's Algorithm?
Answer: For arbitrary numbers 230, 1908, 9814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.