Highest Common Factor of 8015, 6174 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 8015, 6174 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 8015, 6174 is 7 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 8015, 6174 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 8015, 6174 is 7.
HCF(8015, 6174) = 7
HCF of 8015, 6174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8015, 6174 is 7.
Highest Common Factor of 8015,6174 is 7
Step 1: Since 8015 > 6174, we apply the division lemma to 8015 and 6174, to get
8015 = 6174 x 1 + 1841
Step 2: Since the reminder 6174 ≠ 0, we apply division lemma to 1841 and 6174, to get
6174 = 1841 x 3 + 651
Step 3: We consider the new divisor 1841 and the new remainder 651, and apply the division lemma to get
1841 = 651 x 2 + 539
We consider the new divisor 651 and the new remainder 539,and apply the division lemma to get
651 = 539 x 1 + 112
We consider the new divisor 539 and the new remainder 112,and apply the division lemma to get
539 = 112 x 4 + 91
We consider the new divisor 112 and the new remainder 91,and apply the division lemma to get
112 = 91 x 1 + 21
We consider the new divisor 91 and the new remainder 21,and apply the division lemma to get
91 = 21 x 4 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 8015 and 6174 is 7
Notice that 7 = HCF(21,7) = HCF(91,21) = HCF(112,91) = HCF(539,112) = HCF(651,539) = HCF(1841,651) = HCF(6174,1841) = HCF(8015,6174) .
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Frequently Asked Questions on HCF of 8015, 6174 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 8015, 6174?
Answer: HCF of 8015, 6174 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8015, 6174 using Euclid's Algorithm?
Answer: For arbitrary numbers 8015, 6174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.