Highest Common Factor of 6111, 8540 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 6111, 8540 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 6111, 8540 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 6111, 8540 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 6111, 8540 is 7.
HCF(6111, 8540) = 7
HCF of 6111, 8540 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6111, 8540 is 7.
Highest Common Factor of 6111,8540 is 7
Step 1: Since 8540 > 6111, we apply the division lemma to 8540 and 6111, to get
8540 = 6111 x 1 + 2429
Step 2: Since the reminder 6111 ≠ 0, we apply division lemma to 2429 and 6111, to get
6111 = 2429 x 2 + 1253
Step 3: We consider the new divisor 2429 and the new remainder 1253, and apply the division lemma to get
2429 = 1253 x 1 + 1176
We consider the new divisor 1253 and the new remainder 1176,and apply the division lemma to get
1253 = 1176 x 1 + 77
We consider the new divisor 1176 and the new remainder 77,and apply the division lemma to get
1176 = 77 x 15 + 21
We consider the new divisor 77 and the new remainder 21,and apply the division lemma to get
77 = 21 x 3 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 6111 and 8540 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(77,21) = HCF(1176,77) = HCF(1253,1176) = HCF(2429,1253) = HCF(6111,2429) = HCF(8540,6111) .
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Frequently Asked Questions on HCF of 6111, 8540 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 6111, 8540?
Answer: HCF of 6111, 8540 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6111, 8540 using Euclid's Algorithm?
Answer: For arbitrary numbers 6111, 8540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.