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 8537, 9180, 32838 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8537, 9180, 32838 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 8537, 9180, 32838 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 8537, 9180, 32838 is 1.
HCF(8537, 9180, 32838) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8537, 9180, 32838 is 1.
Step 1: Since 9180 > 8537, we apply the division lemma to 9180 and 8537, to get
9180 = 8537 x 1 + 643
Step 2: Since the reminder 8537 ≠ 0, we apply division lemma to 643 and 8537, to get
8537 = 643 x 13 + 178
Step 3: We consider the new divisor 643 and the new remainder 178, and apply the division lemma to get
643 = 178 x 3 + 109
We consider the new divisor 178 and the new remainder 109,and apply the division lemma to get
178 = 109 x 1 + 69
We consider the new divisor 109 and the new remainder 69,and apply the division lemma to get
109 = 69 x 1 + 40
We consider the new divisor 69 and the new remainder 40,and apply the division lemma to get
69 = 40 x 1 + 29
We consider the new divisor 40 and the new remainder 29,and apply the division lemma to get
40 = 29 x 1 + 11
We consider the new divisor 29 and the new remainder 11,and apply the division lemma to get
29 = 11 x 2 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8537 and 9180 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(69,40) = HCF(109,69) = HCF(178,109) = HCF(643,178) = HCF(8537,643) = HCF(9180,8537) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32838 > 1, we apply the division lemma to 32838 and 1, to get
32838 = 1 x 32838 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32838 is 1
Notice that 1 = HCF(32838,1) .
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 8537, 9180, 32838?
Answer: HCF of 8537, 9180, 32838 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8537, 9180, 32838 using Euclid's Algorithm?
Answer: For arbitrary numbers 8537, 9180, 32838 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.