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 1977, 2820, 90233 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1977, 2820, 90233 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 1977, 2820, 90233 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 1977, 2820, 90233 is 1.
HCF(1977, 2820, 90233) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1977, 2820, 90233 is 1.
Step 1: Since 2820 > 1977, we apply the division lemma to 2820 and 1977, to get
2820 = 1977 x 1 + 843
Step 2: Since the reminder 1977 ≠ 0, we apply division lemma to 843 and 1977, to get
1977 = 843 x 2 + 291
Step 3: We consider the new divisor 843 and the new remainder 291, and apply the division lemma to get
843 = 291 x 2 + 261
We consider the new divisor 291 and the new remainder 261,and apply the division lemma to get
291 = 261 x 1 + 30
We consider the new divisor 261 and the new remainder 30,and apply the division lemma to get
261 = 30 x 8 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1977 and 2820 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(261,30) = HCF(291,261) = HCF(843,291) = HCF(1977,843) = HCF(2820,1977) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 90233 > 3, we apply the division lemma to 90233 and 3, to get
90233 = 3 x 30077 + 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 90233 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(90233,3) .
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 1977, 2820, 90233?
Answer: HCF of 1977, 2820, 90233 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1977, 2820, 90233 using Euclid's Algorithm?
Answer: For arbitrary numbers 1977, 2820, 90233 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.