Highest Common Factor of 5040, 9084 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 5040, 9084 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 5040, 9084 is 12 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 5040, 9084 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 5040, 9084 is 12.
HCF(5040, 9084) = 12
HCF of 5040, 9084 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 5040, 9084 is 12.
Highest Common Factor of 5040,9084 is 12
Step 1: Since 9084 > 5040, we apply the division lemma to 9084 and 5040, to get
9084 = 5040 x 1 + 4044
Step 2: Since the reminder 5040 ≠ 0, we apply division lemma to 4044 and 5040, to get
5040 = 4044 x 1 + 996
Step 3: We consider the new divisor 4044 and the new remainder 996, and apply the division lemma to get
4044 = 996 x 4 + 60
We consider the new divisor 996 and the new remainder 60,and apply the division lemma to get
996 = 60 x 16 + 36
We consider the new divisor 60 and the new remainder 36,and apply the division lemma to get
60 = 36 x 1 + 24
We consider the new divisor 36 and the new remainder 24,and apply the division lemma to get
36 = 24 x 1 + 12
We consider the new divisor 24 and the new remainder 12,and apply the division lemma to get
24 = 12 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 5040 and 9084 is 12
Notice that 12 = HCF(24,12) = HCF(36,24) = HCF(60,36) = HCF(996,60) = HCF(4044,996) = HCF(5040,4044) = HCF(9084,5040) .
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Frequently Asked Questions on HCF of 5040, 9084 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 5040, 9084?
Answer: HCF of 5040, 9084 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 5040, 9084 using Euclid's Algorithm?
Answer: For arbitrary numbers 5040, 9084 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
