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 820, 3203, 9218 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 820, 3203, 9218 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 820, 3203, 9218 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 820, 3203, 9218 is 1.
HCF(820, 3203, 9218) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 820, 3203, 9218 is 1.
Step 1: Since 3203 > 820, we apply the division lemma to 3203 and 820, to get
3203 = 820 x 3 + 743
Step 2: Since the reminder 820 ≠ 0, we apply division lemma to 743 and 820, to get
820 = 743 x 1 + 77
Step 3: We consider the new divisor 743 and the new remainder 77, and apply the division lemma to get
743 = 77 x 9 + 50
We consider the new divisor 77 and the new remainder 50,and apply the division lemma to get
77 = 50 x 1 + 27
We consider the new divisor 50 and the new remainder 27,and apply the division lemma to get
50 = 27 x 1 + 23
We consider the new divisor 27 and the new remainder 23,and apply the division lemma to get
27 = 23 x 1 + 4
We consider the new divisor 23 and the new remainder 4,and apply the division lemma to get
23 = 4 x 5 + 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 820 and 3203 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(27,23) = HCF(50,27) = HCF(77,50) = HCF(743,77) = HCF(820,743) = HCF(3203,820) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9218 > 1, we apply the division lemma to 9218 and 1, to get
9218 = 1 x 9218 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 9218 is 1
Notice that 1 = HCF(9218,1) .
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 820, 3203, 9218?
Answer: HCF of 820, 3203, 9218 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 820, 3203, 9218 using Euclid's Algorithm?
Answer: For arbitrary numbers 820, 3203, 9218 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.