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 822, 243, 980 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 822, 243, 980 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 822, 243, 980 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 822, 243, 980 is 1.
HCF(822, 243, 980) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 822, 243, 980 is 1.
Step 1: Since 822 > 243, we apply the division lemma to 822 and 243, to get
822 = 243 x 3 + 93
Step 2: Since the reminder 243 ≠ 0, we apply division lemma to 93 and 243, to get
243 = 93 x 2 + 57
Step 3: We consider the new divisor 93 and the new remainder 57, and apply the division lemma to get
93 = 57 x 1 + 36
We consider the new divisor 57 and the new remainder 36,and apply the division lemma to get
57 = 36 x 1 + 21
We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get
36 = 21 x 1 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 822 and 243 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(57,36) = HCF(93,57) = HCF(243,93) = HCF(822,243) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 980 > 3, we apply the division lemma to 980 and 3, to get
980 = 3 x 326 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 980 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(980,3) .
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 822, 243, 980?
Answer: HCF of 822, 243, 980 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 822, 243, 980 using Euclid's Algorithm?
Answer: For arbitrary numbers 822, 243, 980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.