Highest Common Factor of 2994, 8640 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 2994, 8640 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2994, 8640 is 6 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 2994, 8640 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 2994, 8640 is 6.
HCF(2994, 8640) = 6
HCF of 2994, 8640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2994, 8640 is 6.
Highest Common Factor of 2994,8640 is 6
Step 1: Since 8640 > 2994, we apply the division lemma to 8640 and 2994, to get
8640 = 2994 x 2 + 2652
Step 2: Since the reminder 2994 ≠ 0, we apply division lemma to 2652 and 2994, to get
2994 = 2652 x 1 + 342
Step 3: We consider the new divisor 2652 and the new remainder 342, and apply the division lemma to get
2652 = 342 x 7 + 258
We consider the new divisor 342 and the new remainder 258,and apply the division lemma to get
342 = 258 x 1 + 84
We consider the new divisor 258 and the new remainder 84,and apply the division lemma to get
258 = 84 x 3 + 6
We consider the new divisor 84 and the new remainder 6,and apply the division lemma to get
84 = 6 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2994 and 8640 is 6
Notice that 6 = HCF(84,6) = HCF(258,84) = HCF(342,258) = HCF(2652,342) = HCF(2994,2652) = HCF(8640,2994) .
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Frequently Asked Questions on HCF of 2994, 8640 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 2994, 8640?
Answer: HCF of 2994, 8640 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2994, 8640 using Euclid's Algorithm?
Answer: For arbitrary numbers 2994, 8640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.