Highest Common Factor of 9930, 5307, 66123 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 9930, 5307, 66123 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9930, 5307, 66123 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 9930, 5307, 66123 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 9930, 5307, 66123 is 3.
HCF(9930, 5307, 66123) = 3
HCF of 9930, 5307, 66123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9930, 5307, 66123 is 3.
Highest Common Factor of 9930,5307,66123 is 3
Step 1: Since 9930 > 5307, we apply the division lemma to 9930 and 5307, to get
9930 = 5307 x 1 + 4623
Step 2: Since the reminder 5307 ≠ 0, we apply division lemma to 4623 and 5307, to get
5307 = 4623 x 1 + 684
Step 3: We consider the new divisor 4623 and the new remainder 684, and apply the division lemma to get
4623 = 684 x 6 + 519
We consider the new divisor 684 and the new remainder 519,and apply the division lemma to get
684 = 519 x 1 + 165
We consider the new divisor 519 and the new remainder 165,and apply the division lemma to get
519 = 165 x 3 + 24
We consider the new divisor 165 and the new remainder 24,and apply the division lemma to get
165 = 24 x 6 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9930 and 5307 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(165,24) = HCF(519,165) = HCF(684,519) = HCF(4623,684) = HCF(5307,4623) = HCF(9930,5307) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66123 > 3, we apply the division lemma to 66123 and 3, to get
66123 = 3 x 22041 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 66123 is 3
Notice that 3 = HCF(66123,3) .
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Frequently Asked Questions on HCF of 9930, 5307, 66123 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 9930, 5307, 66123?
Answer: HCF of 9930, 5307, 66123 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9930, 5307, 66123 using Euclid's Algorithm?
Answer: For arbitrary numbers 9930, 5307, 66123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.