Highest Common Factor of 9231, 1914 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 9231, 1914 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9231, 1914 is 3 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 9231, 1914 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 9231, 1914 is 3.
HCF(9231, 1914) = 3
HCF of 9231, 1914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9231, 1914 is 3.
Highest Common Factor of 9231,1914 is 3
Step 1: Since 9231 > 1914, we apply the division lemma to 9231 and 1914, to get
9231 = 1914 x 4 + 1575
Step 2: Since the reminder 1914 ≠ 0, we apply division lemma to 1575 and 1914, to get
1914 = 1575 x 1 + 339
Step 3: We consider the new divisor 1575 and the new remainder 339, and apply the division lemma to get
1575 = 339 x 4 + 219
We consider the new divisor 339 and the new remainder 219,and apply the division lemma to get
339 = 219 x 1 + 120
We consider the new divisor 219 and the new remainder 120,and apply the division lemma to get
219 = 120 x 1 + 99
We consider the new divisor 120 and the new remainder 99,and apply the division lemma to get
120 = 99 x 1 + 21
We consider the new divisor 99 and the new remainder 21,and apply the division lemma to get
99 = 21 x 4 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9231 and 1914 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(99,21) = HCF(120,99) = HCF(219,120) = HCF(339,219) = HCF(1575,339) = HCF(1914,1575) = HCF(9231,1914) .
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Frequently Asked Questions on HCF of 9231, 1914 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 9231, 1914?
Answer: HCF of 9231, 1914 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9231, 1914 using Euclid's Algorithm?
Answer: For arbitrary numbers 9231, 1914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.