Highest Common Factor of 9585, 9685, 38428 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 9585, 9685, 38428 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9585, 9685, 38428 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 9585, 9685, 38428 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 9585, 9685, 38428 is 1.
HCF(9585, 9685, 38428) = 1
HCF of 9585, 9685, 38428 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9585, 9685, 38428 is 1.
Highest Common Factor of 9585,9685,38428 is 1
Step 1: Since 9685 > 9585, we apply the division lemma to 9685 and 9585, to get
9685 = 9585 x 1 + 100
Step 2: Since the reminder 9585 ≠ 0, we apply division lemma to 100 and 9585, to get
9585 = 100 x 95 + 85
Step 3: We consider the new divisor 100 and the new remainder 85, and apply the division lemma to get
100 = 85 x 1 + 15
We consider the new divisor 85 and the new remainder 15,and apply the division lemma to get
85 = 15 x 5 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 9585 and 9685 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(85,15) = HCF(100,85) = HCF(9585,100) = HCF(9685,9585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38428 > 5, we apply the division lemma to 38428 and 5, to get
38428 = 5 x 7685 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 38428 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(38428,5) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9585, 9685, 38428 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 9585, 9685, 38428?
Answer: HCF of 9585, 9685, 38428 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9585, 9685, 38428 using Euclid's Algorithm?
Answer: For arbitrary numbers 9585, 9685, 38428 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.