Highest Common Factor of 9986, 2918, 17330 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 9986, 2918, 17330 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 9986, 2918, 17330 is 2 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 9986, 2918, 17330 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 9986, 2918, 17330 is 2.
HCF(9986, 2918, 17330) = 2
HCF of 9986, 2918, 17330 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9986, 2918, 17330 is 2.
Highest Common Factor of 9986,2918,17330 is 2
Step 1: Since 9986 > 2918, we apply the division lemma to 9986 and 2918, to get
9986 = 2918 x 3 + 1232
Step 2: Since the reminder 2918 ≠ 0, we apply division lemma to 1232 and 2918, to get
2918 = 1232 x 2 + 454
Step 3: We consider the new divisor 1232 and the new remainder 454, and apply the division lemma to get
1232 = 454 x 2 + 324
We consider the new divisor 454 and the new remainder 324,and apply the division lemma to get
454 = 324 x 1 + 130
We consider the new divisor 324 and the new remainder 130,and apply the division lemma to get
324 = 130 x 2 + 64
We consider the new divisor 130 and the new remainder 64,and apply the division lemma to get
130 = 64 x 2 + 2
We consider the new divisor 64 and the new remainder 2,and apply the division lemma to get
64 = 2 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9986 and 2918 is 2
Notice that 2 = HCF(64,2) = HCF(130,64) = HCF(324,130) = HCF(454,324) = HCF(1232,454) = HCF(2918,1232) = HCF(9986,2918) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 17330 > 2, we apply the division lemma to 17330 and 2, to get
17330 = 2 x 8665 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 17330 is 2
Notice that 2 = HCF(17330,2) .
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Frequently Asked Questions on HCF of 9986, 2918, 17330 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 9986, 2918, 17330?
Answer: HCF of 9986, 2918, 17330 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9986, 2918, 17330 using Euclid's Algorithm?
Answer: For arbitrary numbers 9986, 2918, 17330 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.