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 8441, 4281, 19525 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8441, 4281, 19525 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 8441, 4281, 19525 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 8441, 4281, 19525 is 1.
HCF(8441, 4281, 19525) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8441, 4281, 19525 is 1.
Step 1: Since 8441 > 4281, we apply the division lemma to 8441 and 4281, to get
8441 = 4281 x 1 + 4160
Step 2: Since the reminder 4281 ≠ 0, we apply division lemma to 4160 and 4281, to get
4281 = 4160 x 1 + 121
Step 3: We consider the new divisor 4160 and the new remainder 121, and apply the division lemma to get
4160 = 121 x 34 + 46
We consider the new divisor 121 and the new remainder 46,and apply the division lemma to get
121 = 46 x 2 + 29
We consider the new divisor 46 and the new remainder 29,and apply the division lemma to get
46 = 29 x 1 + 17
We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get
29 = 17 x 1 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 8441 and 4281 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(46,29) = HCF(121,46) = HCF(4160,121) = HCF(4281,4160) = HCF(8441,4281) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 19525 > 1, we apply the division lemma to 19525 and 1, to get
19525 = 1 x 19525 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 19525 is 1
Notice that 1 = HCF(19525,1) .
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 8441, 4281, 19525?
Answer: HCF of 8441, 4281, 19525 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8441, 4281, 19525 using Euclid's Algorithm?
Answer: For arbitrary numbers 8441, 4281, 19525 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.