Highest Common Factor of 9822, 6144 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 9822, 6144 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 9822, 6144 is 6 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 9822, 6144 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 9822, 6144 is 6.
HCF(9822, 6144) = 6
HCF of 9822, 6144 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9822, 6144 is 6.
Highest Common Factor of 9822,6144 is 6
Step 1: Since 9822 > 6144, we apply the division lemma to 9822 and 6144, to get
9822 = 6144 x 1 + 3678
Step 2: Since the reminder 6144 ≠ 0, we apply division lemma to 3678 and 6144, to get
6144 = 3678 x 1 + 2466
Step 3: We consider the new divisor 3678 and the new remainder 2466, and apply the division lemma to get
3678 = 2466 x 1 + 1212
We consider the new divisor 2466 and the new remainder 1212,and apply the division lemma to get
2466 = 1212 x 2 + 42
We consider the new divisor 1212 and the new remainder 42,and apply the division lemma to get
1212 = 42 x 28 + 36
We consider the new divisor 42 and the new remainder 36,and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 9822 and 6144 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(1212,42) = HCF(2466,1212) = HCF(3678,2466) = HCF(6144,3678) = HCF(9822,6144) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 9822, 6144 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 9822, 6144?
Answer: HCF of 9822, 6144 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9822, 6144 using Euclid's Algorithm?
Answer: For arbitrary numbers 9822, 6144 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.