Highest Common Factor of 8439, 8568, 60405 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 8439, 8568, 60405 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8439, 8568, 60405 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 8439, 8568, 60405 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 8439, 8568, 60405 is 3.
HCF(8439, 8568, 60405) = 3
HCF of 8439, 8568, 60405 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8439, 8568, 60405 is 3.
Highest Common Factor of 8439,8568,60405 is 3
Step 1: Since 8568 > 8439, we apply the division lemma to 8568 and 8439, to get
8568 = 8439 x 1 + 129
Step 2: Since the reminder 8439 ≠ 0, we apply division lemma to 129 and 8439, to get
8439 = 129 x 65 + 54
Step 3: We consider the new divisor 129 and the new remainder 54, and apply the division lemma to get
129 = 54 x 2 + 21
We consider the new divisor 54 and the new remainder 21,and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 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 8439 and 8568 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(129,54) = HCF(8439,129) = HCF(8568,8439) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60405 > 3, we apply the division lemma to 60405 and 3, to get
60405 = 3 x 20135 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 60405 is 3
Notice that 3 = HCF(60405,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8439, 8568, 60405 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 8439, 8568, 60405?
Answer: HCF of 8439, 8568, 60405 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8439, 8568, 60405 using Euclid's Algorithm?
Answer: For arbitrary numbers 8439, 8568, 60405 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.