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 5509, 6582, 84180 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5509, 6582, 84180 is 1 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 5509, 6582, 84180 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 5509, 6582, 84180 is 1.
HCF(5509, 6582, 84180) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5509, 6582, 84180 is 1.
Step 1: Since 6582 > 5509, we apply the division lemma to 6582 and 5509, to get
6582 = 5509 x 1 + 1073
Step 2: Since the reminder 5509 ≠ 0, we apply division lemma to 1073 and 5509, to get
5509 = 1073 x 5 + 144
Step 3: We consider the new divisor 1073 and the new remainder 144, and apply the division lemma to get
1073 = 144 x 7 + 65
We consider the new divisor 144 and the new remainder 65,and apply the division lemma to get
144 = 65 x 2 + 14
We consider the new divisor 65 and the new remainder 14,and apply the division lemma to get
65 = 14 x 4 + 9
We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get
14 = 9 x 1 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5509 and 6582 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(65,14) = HCF(144,65) = HCF(1073,144) = HCF(5509,1073) = HCF(6582,5509) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84180 > 1, we apply the division lemma to 84180 and 1, to get
84180 = 1 x 84180 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84180 is 1
Notice that 1 = HCF(84180,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 5509, 6582, 84180?
Answer: HCF of 5509, 6582, 84180 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5509, 6582, 84180 using Euclid's Algorithm?
Answer: For arbitrary numbers 5509, 6582, 84180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.