Highest Common Factor of 9120, 5739, 59697 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 9120, 5739, 59697 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 9120, 5739, 59697 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 9120, 5739, 59697 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 9120, 5739, 59697 is 3.
HCF(9120, 5739, 59697) = 3
HCF of 9120, 5739, 59697 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9120, 5739, 59697 is 3.
Highest Common Factor of 9120,5739,59697 is 3
Step 1: Since 9120 > 5739, we apply the division lemma to 9120 and 5739, to get
9120 = 5739 x 1 + 3381
Step 2: Since the reminder 5739 ≠ 0, we apply division lemma to 3381 and 5739, to get
5739 = 3381 x 1 + 2358
Step 3: We consider the new divisor 3381 and the new remainder 2358, and apply the division lemma to get
3381 = 2358 x 1 + 1023
We consider the new divisor 2358 and the new remainder 1023,and apply the division lemma to get
2358 = 1023 x 2 + 312
We consider the new divisor 1023 and the new remainder 312,and apply the division lemma to get
1023 = 312 x 3 + 87
We consider the new divisor 312 and the new remainder 87,and apply the division lemma to get
312 = 87 x 3 + 51
We consider the new divisor 87 and the new remainder 51,and apply the division lemma to get
87 = 51 x 1 + 36
We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get
51 = 36 x 1 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9120 and 5739 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(87,51) = HCF(312,87) = HCF(1023,312) = HCF(2358,1023) = HCF(3381,2358) = HCF(5739,3381) = HCF(9120,5739) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 59697 > 3, we apply the division lemma to 59697 and 3, to get
59697 = 3 x 19899 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 59697 is 3
Notice that 3 = HCF(59697,3) .
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Frequently Asked Questions on HCF of 9120, 5739, 59697 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 9120, 5739, 59697?
Answer: HCF of 9120, 5739, 59697 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9120, 5739, 59697 using Euclid's Algorithm?
Answer: For arbitrary numbers 9120, 5739, 59697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
