Highest Common Factor of 302, 2069 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, 2069 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 302, 2069 is 1 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, 2069 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, 2069 is 1.
HCF(302, 2069) = 1
HCF of 302, 2069 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, 2069 is 1.
Highest Common Factor of 302,2069 is 1
Step 1: Since 2069 > 302, we apply the division lemma to 2069 and 302, to get
2069 = 302 x 6 + 257
Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 257 and 302, to get
302 = 257 x 1 + 45
Step 3: We consider the new divisor 257 and the new remainder 45, and apply the division lemma to get
257 = 45 x 5 + 32
We consider the new divisor 45 and the new remainder 32,and apply the division lemma to get
45 = 32 x 1 + 13
We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get
32 = 13 x 2 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 302 and 2069 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(45,32) = HCF(257,45) = HCF(302,257) = HCF(2069,302) .
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Frequently Asked Questions on HCF of 302, 2069 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, 2069?
Answer: HCF of 302, 2069 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 302, 2069 using Euclid's Algorithm?
Answer: For arbitrary numbers 302, 2069 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.