Highest Common Factor of 9132, 2314 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 9132, 2314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9132, 2314 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 9132, 2314 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 9132, 2314 is 2.
HCF(9132, 2314) = 2
HCF of 9132, 2314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9132, 2314 is 2.
Highest Common Factor of 9132,2314 is 2
Step 1: Since 9132 > 2314, we apply the division lemma to 9132 and 2314, to get
9132 = 2314 x 3 + 2190
Step 2: Since the reminder 2314 ≠ 0, we apply division lemma to 2190 and 2314, to get
2314 = 2190 x 1 + 124
Step 3: We consider the new divisor 2190 and the new remainder 124, and apply the division lemma to get
2190 = 124 x 17 + 82
We consider the new divisor 124 and the new remainder 82,and apply the division lemma to get
124 = 82 x 1 + 42
We consider the new divisor 82 and the new remainder 42,and apply the division lemma to get
82 = 42 x 1 + 40
We consider the new divisor 42 and the new remainder 40,and apply the division lemma to get
42 = 40 x 1 + 2
We consider the new divisor 40 and the new remainder 2,and apply the division lemma to get
40 = 2 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9132 and 2314 is 2
Notice that 2 = HCF(40,2) = HCF(42,40) = HCF(82,42) = HCF(124,82) = HCF(2190,124) = HCF(2314,2190) = HCF(9132,2314) .
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Frequently Asked Questions on HCF of 9132, 2314 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 9132, 2314?
Answer: HCF of 9132, 2314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9132, 2314 using Euclid's Algorithm?
Answer: For arbitrary numbers 9132, 2314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.