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 8696, 2322, 48771 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8696, 2322, 48771 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 8696, 2322, 48771 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 8696, 2322, 48771 is 1.
HCF(8696, 2322, 48771) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8696, 2322, 48771 is 1.
Step 1: Since 8696 > 2322, we apply the division lemma to 8696 and 2322, to get
8696 = 2322 x 3 + 1730
Step 2: Since the reminder 2322 ≠ 0, we apply division lemma to 1730 and 2322, to get
2322 = 1730 x 1 + 592
Step 3: We consider the new divisor 1730 and the new remainder 592, and apply the division lemma to get
1730 = 592 x 2 + 546
We consider the new divisor 592 and the new remainder 546,and apply the division lemma to get
592 = 546 x 1 + 46
We consider the new divisor 546 and the new remainder 46,and apply the division lemma to get
546 = 46 x 11 + 40
We consider the new divisor 46 and the new remainder 40,and apply the division lemma to get
46 = 40 x 1 + 6
We consider the new divisor 40 and the new remainder 6,and apply the division lemma to get
40 = 6 x 6 + 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 8696 and 2322 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(40,6) = HCF(46,40) = HCF(546,46) = HCF(592,546) = HCF(1730,592) = HCF(2322,1730) = HCF(8696,2322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 48771 > 2, we apply the division lemma to 48771 and 2, to get
48771 = 2 x 24385 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 48771 is 1
Notice that 1 = HCF(2,1) = HCF(48771,2) .
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 8696, 2322, 48771?
Answer: HCF of 8696, 2322, 48771 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8696, 2322, 48771 using Euclid's Algorithm?
Answer: For arbitrary numbers 8696, 2322, 48771 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.