Highest Common Factor of 6666, 6314, 16627 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 6666, 6314, 16627 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6666, 6314, 16627 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 6666, 6314, 16627 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 6666, 6314, 16627 is 1.
HCF(6666, 6314, 16627) = 1
HCF of 6666, 6314, 16627 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6666, 6314, 16627 is 1.
Highest Common Factor of 6666,6314,16627 is 1
Step 1: Since 6666 > 6314, we apply the division lemma to 6666 and 6314, to get
6666 = 6314 x 1 + 352
Step 2: Since the reminder 6314 ≠ 0, we apply division lemma to 352 and 6314, to get
6314 = 352 x 17 + 330
Step 3: We consider the new divisor 352 and the new remainder 330, and apply the division lemma to get
352 = 330 x 1 + 22
We consider the new divisor 330 and the new remainder 22, and apply the division lemma to get
330 = 22 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 6666 and 6314 is 22
Notice that 22 = HCF(330,22) = HCF(352,330) = HCF(6314,352) = HCF(6666,6314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16627 > 22, we apply the division lemma to 16627 and 22, to get
16627 = 22 x 755 + 17
Step 2: Since the reminder 22 ≠ 0, we apply division lemma to 17 and 22, to get
22 = 17 x 1 + 5
Step 3: We consider the new divisor 17 and the new remainder 5, and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 22 and 16627 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(16627,22) .
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Frequently Asked Questions on HCF of 6666, 6314, 16627 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 6666, 6314, 16627?
Answer: HCF of 6666, 6314, 16627 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6666, 6314, 16627 using Euclid's Algorithm?
Answer: For arbitrary numbers 6666, 6314, 16627 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
