Highest Common Factor of 302, 2008 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 302, 2008 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 302, 2008 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 302, 2008 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 302, 2008 is 2.
HCF(302, 2008) = 2
HCF of 302, 2008 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 302, 2008 is 2.
Highest Common Factor of 302,2008 is 2
Step 1: Since 2008 > 302, we apply the division lemma to 2008 and 302, to get
2008 = 302 x 6 + 196
Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 196 and 302, to get
302 = 196 x 1 + 106
Step 3: We consider the new divisor 196 and the new remainder 106, and apply the division lemma to get
196 = 106 x 1 + 90
We consider the new divisor 106 and the new remainder 90,and apply the division lemma to get
106 = 90 x 1 + 16
We consider the new divisor 90 and the new remainder 16,and apply the division lemma to get
90 = 16 x 5 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 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 302 and 2008 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(90,16) = HCF(106,90) = HCF(196,106) = HCF(302,196) = HCF(2008,302) .
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Frequently Asked Questions on HCF of 302, 2008 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 302, 2008?
Answer: HCF of 302, 2008 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 302, 2008 using Euclid's Algorithm?
Answer: For arbitrary numbers 302, 2008 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.