Highest Common Factor of 2415, 4341, 69120 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 2415, 4341, 69120 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2415, 4341, 69120 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 2415, 4341, 69120 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 2415, 4341, 69120 is 3.
HCF(2415, 4341, 69120) = 3
HCF of 2415, 4341, 69120 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2415, 4341, 69120 is 3.
Highest Common Factor of 2415,4341,69120 is 3
Step 1: Since 4341 > 2415, we apply the division lemma to 4341 and 2415, to get
4341 = 2415 x 1 + 1926
Step 2: Since the reminder 2415 ≠ 0, we apply division lemma to 1926 and 2415, to get
2415 = 1926 x 1 + 489
Step 3: We consider the new divisor 1926 and the new remainder 489, and apply the division lemma to get
1926 = 489 x 3 + 459
We consider the new divisor 489 and the new remainder 459,and apply the division lemma to get
489 = 459 x 1 + 30
We consider the new divisor 459 and the new remainder 30,and apply the division lemma to get
459 = 30 x 15 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2415 and 4341 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(459,30) = HCF(489,459) = HCF(1926,489) = HCF(2415,1926) = HCF(4341,2415) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69120 > 3, we apply the division lemma to 69120 and 3, to get
69120 = 3 x 23040 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 69120 is 3
Notice that 3 = HCF(69120,3) .
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Frequently Asked Questions on HCF of 2415, 4341, 69120 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 2415, 4341, 69120?
Answer: HCF of 2415, 4341, 69120 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2415, 4341, 69120 using Euclid's Algorithm?
Answer: For arbitrary numbers 2415, 4341, 69120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.