Highest Common Factor of 9006, 2144, 79984 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 9006, 2144, 79984 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9006, 2144, 79984 is 2 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 9006, 2144, 79984 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 9006, 2144, 79984 is 2.
HCF(9006, 2144, 79984) = 2
HCF of 9006, 2144, 79984 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9006, 2144, 79984 is 2.
Highest Common Factor of 9006,2144,79984 is 2
Step 1: Since 9006 > 2144, we apply the division lemma to 9006 and 2144, to get
9006 = 2144 x 4 + 430
Step 2: Since the reminder 2144 ≠ 0, we apply division lemma to 430 and 2144, to get
2144 = 430 x 4 + 424
Step 3: We consider the new divisor 430 and the new remainder 424, and apply the division lemma to get
430 = 424 x 1 + 6
We consider the new divisor 424 and the new remainder 6,and apply the division lemma to get
424 = 6 x 70 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9006 and 2144 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(424,6) = HCF(430,424) = HCF(2144,430) = HCF(9006,2144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 79984 > 2, we apply the division lemma to 79984 and 2, to get
79984 = 2 x 39992 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 79984 is 2
Notice that 2 = HCF(79984,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9006, 2144, 79984 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 9006, 2144, 79984?
Answer: HCF of 9006, 2144, 79984 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9006, 2144, 79984 using Euclid's Algorithm?
Answer: For arbitrary numbers 9006, 2144, 79984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.