Highest Common Factor of 2688, 2073, 66963 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 2688, 2073, 66963 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2688, 2073, 66963 is 3 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 2688, 2073, 66963 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 2688, 2073, 66963 is 3.
HCF(2688, 2073, 66963) = 3
HCF of 2688, 2073, 66963 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2688, 2073, 66963 is 3.
Highest Common Factor of 2688,2073,66963 is 3
Step 1: Since 2688 > 2073, we apply the division lemma to 2688 and 2073, to get
2688 = 2073 x 1 + 615
Step 2: Since the reminder 2073 ≠ 0, we apply division lemma to 615 and 2073, to get
2073 = 615 x 3 + 228
Step 3: We consider the new divisor 615 and the new remainder 228, and apply the division lemma to get
615 = 228 x 2 + 159
We consider the new divisor 228 and the new remainder 159,and apply the division lemma to get
228 = 159 x 1 + 69
We consider the new divisor 159 and the new remainder 69,and apply the division lemma to get
159 = 69 x 2 + 21
We consider the new divisor 69 and the new remainder 21,and apply the division lemma to get
69 = 21 x 3 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2688 and 2073 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(69,21) = HCF(159,69) = HCF(228,159) = HCF(615,228) = HCF(2073,615) = HCF(2688,2073) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66963 > 3, we apply the division lemma to 66963 and 3, to get
66963 = 3 x 22321 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 66963 is 3
Notice that 3 = HCF(66963,3) .
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Frequently Asked Questions on HCF of 2688, 2073, 66963 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 2688, 2073, 66963?
Answer: HCF of 2688, 2073, 66963 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2688, 2073, 66963 using Euclid's Algorithm?
Answer: For arbitrary numbers 2688, 2073, 66963 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.