Highest Common Factor of 288, 2470 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 288, 2470 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 2470 is 2 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 288, 2470 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 288, 2470 is 2.
HCF(288, 2470) = 2
HCF of 288, 2470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 288, 2470 is 2.
Highest Common Factor of 288,2470 is 2
Step 1: Since 2470 > 288, we apply the division lemma to 2470 and 288, to get
2470 = 288 x 8 + 166
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 166 and 288, to get
288 = 166 x 1 + 122
Step 3: We consider the new divisor 166 and the new remainder 122, and apply the division lemma to get
166 = 122 x 1 + 44
We consider the new divisor 122 and the new remainder 44,and apply the division lemma to get
122 = 44 x 2 + 34
We consider the new divisor 44 and the new remainder 34,and apply the division lemma to get
44 = 34 x 1 + 10
We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get
34 = 10 x 3 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 288 and 2470 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(44,34) = HCF(122,44) = HCF(166,122) = HCF(288,166) = HCF(2470,288) .
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Frequently Asked Questions on HCF of 288, 2470 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 288, 2470?
Answer: HCF of 288, 2470 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 2470 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 2470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.