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 809, 2322, 1020 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 809, 2322, 1020 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 809, 2322, 1020 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 809, 2322, 1020 is 1.
HCF(809, 2322, 1020) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 809, 2322, 1020 is 1.
Step 1: Since 2322 > 809, we apply the division lemma to 2322 and 809, to get
2322 = 809 x 2 + 704
Step 2: Since the reminder 809 ≠ 0, we apply division lemma to 704 and 809, to get
809 = 704 x 1 + 105
Step 3: We consider the new divisor 704 and the new remainder 105, and apply the division lemma to get
704 = 105 x 6 + 74
We consider the new divisor 105 and the new remainder 74,and apply the division lemma to get
105 = 74 x 1 + 31
We consider the new divisor 74 and the new remainder 31,and apply the division lemma to get
74 = 31 x 2 + 12
We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get
31 = 12 x 2 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 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 809 and 2322 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(74,31) = HCF(105,74) = HCF(704,105) = HCF(809,704) = HCF(2322,809) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1020 > 1, we apply the division lemma to 1020 and 1, to get
1020 = 1 x 1020 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1020 is 1
Notice that 1 = HCF(1020,1) .
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 809, 2322, 1020?
Answer: HCF of 809, 2322, 1020 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 809, 2322, 1020 using Euclid's Algorithm?
Answer: For arbitrary numbers 809, 2322, 1020 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.