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 384, 9798, 5782 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 384, 9798, 5782 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 384, 9798, 5782 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 384, 9798, 5782 is 2.
HCF(384, 9798, 5782) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 384, 9798, 5782 is 2.
Step 1: Since 9798 > 384, we apply the division lemma to 9798 and 384, to get
9798 = 384 x 25 + 198
Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 198 and 384, to get
384 = 198 x 1 + 186
Step 3: We consider the new divisor 198 and the new remainder 186, and apply the division lemma to get
198 = 186 x 1 + 12
We consider the new divisor 186 and the new remainder 12,and apply the division lemma to get
186 = 12 x 15 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 384 and 9798 is 6
Notice that 6 = HCF(12,6) = HCF(186,12) = HCF(198,186) = HCF(384,198) = HCF(9798,384) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5782 > 6, we apply the division lemma to 5782 and 6, to get
5782 = 6 x 963 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: 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 6 and 5782 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(5782,6) .
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 384, 9798, 5782?
Answer: HCF of 384, 9798, 5782 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 384, 9798, 5782 using Euclid's Algorithm?
Answer: For arbitrary numbers 384, 9798, 5782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.