Highest Common Factor of 9870, 2016, 28623 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 9870, 2016, 28623 i.e. 21 the largest integer that leaves a remainder zero for all numbers.
HCF of 9870, 2016, 28623 is 21 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 9870, 2016, 28623 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 9870, 2016, 28623 is 21.
HCF(9870, 2016, 28623) = 21
HCF of 9870, 2016, 28623 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9870, 2016, 28623 is 21.
Highest Common Factor of 9870,2016,28623 is 21
Step 1: Since 9870 > 2016, we apply the division lemma to 9870 and 2016, to get
9870 = 2016 x 4 + 1806
Step 2: Since the reminder 2016 ≠ 0, we apply division lemma to 1806 and 2016, to get
2016 = 1806 x 1 + 210
Step 3: We consider the new divisor 1806 and the new remainder 210, and apply the division lemma to get
1806 = 210 x 8 + 126
We consider the new divisor 210 and the new remainder 126,and apply the division lemma to get
210 = 126 x 1 + 84
We consider the new divisor 126 and the new remainder 84,and apply the division lemma to get
126 = 84 x 1 + 42
We consider the new divisor 84 and the new remainder 42,and apply the division lemma to get
84 = 42 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 42, the HCF of 9870 and 2016 is 42
Notice that 42 = HCF(84,42) = HCF(126,84) = HCF(210,126) = HCF(1806,210) = HCF(2016,1806) = HCF(9870,2016) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 28623 > 42, we apply the division lemma to 28623 and 42, to get
28623 = 42 x 681 + 21
Step 2: Since the reminder 42 ≠ 0, we apply division lemma to 21 and 42, to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 42 and 28623 is 21
Notice that 21 = HCF(42,21) = HCF(28623,42) .
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Frequently Asked Questions on HCF of 9870, 2016, 28623 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 9870, 2016, 28623?
Answer: HCF of 9870, 2016, 28623 is 21 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9870, 2016, 28623 using Euclid's Algorithm?
Answer: For arbitrary numbers 9870, 2016, 28623 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.