Highest Common Factor of 5145, 8506 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 5145, 8506 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 5145, 8506 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 5145, 8506 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 5145, 8506 is 1.
HCF(5145, 8506) = 1
HCF of 5145, 8506 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5145, 8506 is 1.
Highest Common Factor of 5145,8506 is 1
Step 1: Since 8506 > 5145, we apply the division lemma to 8506 and 5145, to get
8506 = 5145 x 1 + 3361
Step 2: Since the reminder 5145 ≠ 0, we apply division lemma to 3361 and 5145, to get
5145 = 3361 x 1 + 1784
Step 3: We consider the new divisor 3361 and the new remainder 1784, and apply the division lemma to get
3361 = 1784 x 1 + 1577
We consider the new divisor 1784 and the new remainder 1577,and apply the division lemma to get
1784 = 1577 x 1 + 207
We consider the new divisor 1577 and the new remainder 207,and apply the division lemma to get
1577 = 207 x 7 + 128
We consider the new divisor 207 and the new remainder 128,and apply the division lemma to get
207 = 128 x 1 + 79
We consider the new divisor 128 and the new remainder 79,and apply the division lemma to get
128 = 79 x 1 + 49
We consider the new divisor 79 and the new remainder 49,and apply the division lemma to get
79 = 49 x 1 + 30
We consider the new divisor 49 and the new remainder 30,and apply the division lemma to get
49 = 30 x 1 + 19
We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get
30 = 19 x 1 + 11
We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get
19 = 11 x 1 + 8
We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get
11 = 8 x 1 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 5145 and 8506 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(49,30) = HCF(79,49) = HCF(128,79) = HCF(207,128) = HCF(1577,207) = HCF(1784,1577) = HCF(3361,1784) = HCF(5145,3361) = HCF(8506,5145) .
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Frequently Asked Questions on HCF of 5145, 8506 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 5145, 8506?
Answer: HCF of 5145, 8506 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5145, 8506 using Euclid's Algorithm?
Answer: For arbitrary numbers 5145, 8506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.