Highest Common Factor of 5400, 6105, 82470 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 5400, 6105, 82470 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 5400, 6105, 82470 is 15 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 5400, 6105, 82470 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 5400, 6105, 82470 is 15.
HCF(5400, 6105, 82470) = 15
HCF of 5400, 6105, 82470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5400, 6105, 82470 is 15.
Highest Common Factor of 5400,6105,82470 is 15
Step 1: Since 6105 > 5400, we apply the division lemma to 6105 and 5400, to get
6105 = 5400 x 1 + 705
Step 2: Since the reminder 5400 ≠ 0, we apply division lemma to 705 and 5400, to get
5400 = 705 x 7 + 465
Step 3: We consider the new divisor 705 and the new remainder 465, and apply the division lemma to get
705 = 465 x 1 + 240
We consider the new divisor 465 and the new remainder 240,and apply the division lemma to get
465 = 240 x 1 + 225
We consider the new divisor 240 and the new remainder 225,and apply the division lemma to get
240 = 225 x 1 + 15
We consider the new divisor 225 and the new remainder 15,and apply the division lemma to get
225 = 15 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 5400 and 6105 is 15
Notice that 15 = HCF(225,15) = HCF(240,225) = HCF(465,240) = HCF(705,465) = HCF(5400,705) = HCF(6105,5400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 82470 > 15, we apply the division lemma to 82470 and 15, to get
82470 = 15 x 5498 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 15 and 82470 is 15
Notice that 15 = HCF(82470,15) .
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Frequently Asked Questions on HCF of 5400, 6105, 82470 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 5400, 6105, 82470?
Answer: HCF of 5400, 6105, 82470 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5400, 6105, 82470 using Euclid's Algorithm?
Answer: For arbitrary numbers 5400, 6105, 82470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.