Highest Common Factor of 300, 27411 using Euclid's algorithm
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 300, 27411 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 300, 27411 is 3 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 300, 27411 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 300, 27411 is 3.
HCF(300, 27411) = 3
HCF of 300, 27411 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 300, 27411 is 3.
Highest Common Factor of 300,27411 is 3
Step 1: Since 27411 > 300, we apply the division lemma to 27411 and 300, to get
27411 = 300 x 91 + 111
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 111 and 300, to get
300 = 111 x 2 + 78
Step 3: We consider the new divisor 111 and the new remainder 78, and apply the division lemma to get
111 = 78 x 1 + 33
We consider the new divisor 78 and the new remainder 33,and apply the division lemma to get
78 = 33 x 2 + 12
We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 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 300 and 27411 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(78,33) = HCF(111,78) = HCF(300,111) = HCF(27411,300) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 300, 27411 using Euclid's Algorithm
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 300, 27411?
Answer: HCF of 300, 27411 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 300, 27411 using Euclid's Algorithm?
Answer: For arbitrary numbers 300, 27411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
