Highest Common Factor of 471, 2150, 8040 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 471, 2150, 8040 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 471, 2150, 8040 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 471, 2150, 8040 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 471, 2150, 8040 is 1.
HCF(471, 2150, 8040) = 1
HCF of 471, 2150, 8040 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 471, 2150, 8040 is 1.
Highest Common Factor of 471,2150,8040 is 1
Step 1: Since 2150 > 471, we apply the division lemma to 2150 and 471, to get
2150 = 471 x 4 + 266
Step 2: Since the reminder 471 ≠ 0, we apply division lemma to 266 and 471, to get
471 = 266 x 1 + 205
Step 3: We consider the new divisor 266 and the new remainder 205, and apply the division lemma to get
266 = 205 x 1 + 61
We consider the new divisor 205 and the new remainder 61,and apply the division lemma to get
205 = 61 x 3 + 22
We consider the new divisor 61 and the new remainder 22,and apply the division lemma to get
61 = 22 x 2 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 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 471 and 2150 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(61,22) = HCF(205,61) = HCF(266,205) = HCF(471,266) = HCF(2150,471) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8040 > 1, we apply the division lemma to 8040 and 1, to get
8040 = 1 x 8040 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8040 is 1
Notice that 1 = HCF(8040,1) .
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Frequently Asked Questions on HCF of 471, 2150, 8040 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 471, 2150, 8040?
Answer: HCF of 471, 2150, 8040 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 471, 2150, 8040 using Euclid's Algorithm?
Answer: For arbitrary numbers 471, 2150, 8040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
