Highest Common Factor of 8006, 9094, 14317 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 8006, 9094, 14317 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8006, 9094, 14317 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 8006, 9094, 14317 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 8006, 9094, 14317 is 1.
HCF(8006, 9094, 14317) = 1
HCF of 8006, 9094, 14317 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8006, 9094, 14317 is 1.
Highest Common Factor of 8006,9094,14317 is 1
Step 1: Since 9094 > 8006, we apply the division lemma to 9094 and 8006, to get
9094 = 8006 x 1 + 1088
Step 2: Since the reminder 8006 ≠ 0, we apply division lemma to 1088 and 8006, to get
8006 = 1088 x 7 + 390
Step 3: We consider the new divisor 1088 and the new remainder 390, and apply the division lemma to get
1088 = 390 x 2 + 308
We consider the new divisor 390 and the new remainder 308,and apply the division lemma to get
390 = 308 x 1 + 82
We consider the new divisor 308 and the new remainder 82,and apply the division lemma to get
308 = 82 x 3 + 62
We consider the new divisor 82 and the new remainder 62,and apply the division lemma to get
82 = 62 x 1 + 20
We consider the new divisor 62 and the new remainder 20,and apply the division lemma to get
62 = 20 x 3 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8006 and 9094 is 2
Notice that 2 = HCF(20,2) = HCF(62,20) = HCF(82,62) = HCF(308,82) = HCF(390,308) = HCF(1088,390) = HCF(8006,1088) = HCF(9094,8006) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14317 > 2, we apply the division lemma to 14317 and 2, to get
14317 = 2 x 7158 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 14317 is 1
Notice that 1 = HCF(2,1) = HCF(14317,2) .
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Frequently Asked Questions on HCF of 8006, 9094, 14317 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 8006, 9094, 14317?
Answer: HCF of 8006, 9094, 14317 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8006, 9094, 14317 using Euclid's Algorithm?
Answer: For arbitrary numbers 8006, 9094, 14317 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.