Highest Common Factor of 300, 7166, 8411 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, 7166, 8411 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 300, 7166, 8411 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 300, 7166, 8411 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, 7166, 8411 is 1.
HCF(300, 7166, 8411) = 1
HCF of 300, 7166, 8411 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, 7166, 8411 is 1.
Highest Common Factor of 300,7166,8411 is 1
Step 1: Since 7166 > 300, we apply the division lemma to 7166 and 300, to get
7166 = 300 x 23 + 266
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 266 and 300, to get
300 = 266 x 1 + 34
Step 3: We consider the new divisor 266 and the new remainder 34, and apply the division lemma to get
266 = 34 x 7 + 28
We consider the new divisor 34 and the new remainder 28,and apply the division lemma to get
34 = 28 x 1 + 6
We consider the new divisor 28 and the new remainder 6,and apply the division lemma to get
28 = 6 x 4 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 300 and 7166 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(28,6) = HCF(34,28) = HCF(266,34) = HCF(300,266) = HCF(7166,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8411 > 2, we apply the division lemma to 8411 and 2, to get
8411 = 2 x 4205 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 8411 is 1
Notice that 1 = HCF(2,1) = HCF(8411,2) .
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Frequently Asked Questions on HCF of 300, 7166, 8411 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, 7166, 8411?
Answer: HCF of 300, 7166, 8411 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 300, 7166, 8411 using Euclid's Algorithm?
Answer: For arbitrary numbers 300, 7166, 8411 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.