Highest Common Factor of 8103, 6567, 25276 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 8103, 6567, 25276 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8103, 6567, 25276 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 8103, 6567, 25276 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 8103, 6567, 25276 is 1.
HCF(8103, 6567, 25276) = 1
HCF of 8103, 6567, 25276 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8103, 6567, 25276 is 1.
Highest Common Factor of 8103,6567,25276 is 1
Step 1: Since 8103 > 6567, we apply the division lemma to 8103 and 6567, to get
8103 = 6567 x 1 + 1536
Step 2: Since the reminder 6567 ≠ 0, we apply division lemma to 1536 and 6567, to get
6567 = 1536 x 4 + 423
Step 3: We consider the new divisor 1536 and the new remainder 423, and apply the division lemma to get
1536 = 423 x 3 + 267
We consider the new divisor 423 and the new remainder 267,and apply the division lemma to get
423 = 267 x 1 + 156
We consider the new divisor 267 and the new remainder 156,and apply the division lemma to get
267 = 156 x 1 + 111
We consider the new divisor 156 and the new remainder 111,and apply the division lemma to get
156 = 111 x 1 + 45
We consider the new divisor 111 and the new remainder 45,and apply the division lemma to get
111 = 45 x 2 + 21
We consider the new divisor 45 and the new remainder 21,and apply the division lemma to get
45 = 21 x 2 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8103 and 6567 is 3
Notice that 3 = HCF(21,3) = HCF(45,21) = HCF(111,45) = HCF(156,111) = HCF(267,156) = HCF(423,267) = HCF(1536,423) = HCF(6567,1536) = HCF(8103,6567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 25276 > 3, we apply the division lemma to 25276 and 3, to get
25276 = 3 x 8425 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 25276 is 1
Notice that 1 = HCF(3,1) = HCF(25276,3) .
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Frequently Asked Questions on HCF of 8103, 6567, 25276 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 8103, 6567, 25276?
Answer: HCF of 8103, 6567, 25276 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8103, 6567, 25276 using Euclid's Algorithm?
Answer: For arbitrary numbers 8103, 6567, 25276 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.