Highest Common Factor of 2340, 5312 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 2340, 5312 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2340, 5312 is 4 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 2340, 5312 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 2340, 5312 is 4.
HCF(2340, 5312) = 4
HCF of 2340, 5312 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2340, 5312 is 4.
Highest Common Factor of 2340,5312 is 4
Step 1: Since 5312 > 2340, we apply the division lemma to 5312 and 2340, to get
5312 = 2340 x 2 + 632
Step 2: Since the reminder 2340 ≠ 0, we apply division lemma to 632 and 2340, to get
2340 = 632 x 3 + 444
Step 3: We consider the new divisor 632 and the new remainder 444, and apply the division lemma to get
632 = 444 x 1 + 188
We consider the new divisor 444 and the new remainder 188,and apply the division lemma to get
444 = 188 x 2 + 68
We consider the new divisor 188 and the new remainder 68,and apply the division lemma to get
188 = 68 x 2 + 52
We consider the new divisor 68 and the new remainder 52,and apply the division lemma to get
68 = 52 x 1 + 16
We consider the new divisor 52 and the new remainder 16,and apply the division lemma to get
52 = 16 x 3 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2340 and 5312 is 4
Notice that 4 = HCF(16,4) = HCF(52,16) = HCF(68,52) = HCF(188,68) = HCF(444,188) = HCF(632,444) = HCF(2340,632) = HCF(5312,2340) .
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Frequently Asked Questions on HCF of 2340, 5312 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 2340, 5312?
Answer: HCF of 2340, 5312 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2340, 5312 using Euclid's Algorithm?
Answer: For arbitrary numbers 2340, 5312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
