Highest Common Factor of 1608, 8326, 14364 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 1608, 8326, 14364 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1608, 8326, 14364 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 1608, 8326, 14364 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 1608, 8326, 14364 is 2.
HCF(1608, 8326, 14364) = 2
HCF of 1608, 8326, 14364 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1608, 8326, 14364 is 2.
Highest Common Factor of 1608,8326,14364 is 2
Step 1: Since 8326 > 1608, we apply the division lemma to 8326 and 1608, to get
8326 = 1608 x 5 + 286
Step 2: Since the reminder 1608 ≠ 0, we apply division lemma to 286 and 1608, to get
1608 = 286 x 5 + 178
Step 3: We consider the new divisor 286 and the new remainder 178, and apply the division lemma to get
286 = 178 x 1 + 108
We consider the new divisor 178 and the new remainder 108,and apply the division lemma to get
178 = 108 x 1 + 70
We consider the new divisor 108 and the new remainder 70,and apply the division lemma to get
108 = 70 x 1 + 38
We consider the new divisor 70 and the new remainder 38,and apply the division lemma to get
70 = 38 x 1 + 32
We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get
38 = 32 x 1 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 1608 and 8326 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(70,38) = HCF(108,70) = HCF(178,108) = HCF(286,178) = HCF(1608,286) = HCF(8326,1608) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14364 > 2, we apply the division lemma to 14364 and 2, to get
14364 = 2 x 7182 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 14364 is 2
Notice that 2 = HCF(14364,2) .
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Frequently Asked Questions on HCF of 1608, 8326, 14364 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 1608, 8326, 14364?
Answer: HCF of 1608, 8326, 14364 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1608, 8326, 14364 using Euclid's Algorithm?
Answer: For arbitrary numbers 1608, 8326, 14364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.