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 9010, 6807, 12144 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9010, 6807, 12144 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 9010, 6807, 12144 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 9010, 6807, 12144 is 1.
HCF(9010, 6807, 12144) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9010, 6807, 12144 is 1.
Step 1: Since 9010 > 6807, we apply the division lemma to 9010 and 6807, to get
9010 = 6807 x 1 + 2203
Step 2: Since the reminder 6807 ≠ 0, we apply division lemma to 2203 and 6807, to get
6807 = 2203 x 3 + 198
Step 3: We consider the new divisor 2203 and the new remainder 198, and apply the division lemma to get
2203 = 198 x 11 + 25
We consider the new divisor 198 and the new remainder 25,and apply the division lemma to get
198 = 25 x 7 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 9010 and 6807 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(198,25) = HCF(2203,198) = HCF(6807,2203) = HCF(9010,6807) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12144 > 1, we apply the division lemma to 12144 and 1, to get
12144 = 1 x 12144 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12144 is 1
Notice that 1 = HCF(12144,1) .
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 9010, 6807, 12144?
Answer: HCF of 9010, 6807, 12144 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9010, 6807, 12144 using Euclid's Algorithm?
Answer: For arbitrary numbers 9010, 6807, 12144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.