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 9538, 6730, 71171 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9538, 6730, 71171 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 9538, 6730, 71171 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 9538, 6730, 71171 is 1.
HCF(9538, 6730, 71171) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9538, 6730, 71171 is 1.
Step 1: Since 9538 > 6730, we apply the division lemma to 9538 and 6730, to get
9538 = 6730 x 1 + 2808
Step 2: Since the reminder 6730 ≠ 0, we apply division lemma to 2808 and 6730, to get
6730 = 2808 x 2 + 1114
Step 3: We consider the new divisor 2808 and the new remainder 1114, and apply the division lemma to get
2808 = 1114 x 2 + 580
We consider the new divisor 1114 and the new remainder 580,and apply the division lemma to get
1114 = 580 x 1 + 534
We consider the new divisor 580 and the new remainder 534,and apply the division lemma to get
580 = 534 x 1 + 46
We consider the new divisor 534 and the new remainder 46,and apply the division lemma to get
534 = 46 x 11 + 28
We consider the new divisor 46 and the new remainder 28,and apply the division lemma to get
46 = 28 x 1 + 18
We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get
28 = 18 x 1 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9538 and 6730 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(46,28) = HCF(534,46) = HCF(580,534) = HCF(1114,580) = HCF(2808,1114) = HCF(6730,2808) = HCF(9538,6730) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71171 > 2, we apply the division lemma to 71171 and 2, to get
71171 = 2 x 35585 + 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 71171 is 1
Notice that 1 = HCF(2,1) = HCF(71171,2) .
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 9538, 6730, 71171?
Answer: HCF of 9538, 6730, 71171 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9538, 6730, 71171 using Euclid's Algorithm?
Answer: For arbitrary numbers 9538, 6730, 71171 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.