Highest Common Factor of 2269, 7204 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 2269, 7204 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2269, 7204 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 2269, 7204 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 2269, 7204 is 1.
HCF(2269, 7204) = 1
HCF of 2269, 7204 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2269, 7204 is 1.
Highest Common Factor of 2269,7204 is 1
Step 1: Since 7204 > 2269, we apply the division lemma to 7204 and 2269, to get
7204 = 2269 x 3 + 397
Step 2: Since the reminder 2269 ≠ 0, we apply division lemma to 397 and 2269, to get
2269 = 397 x 5 + 284
Step 3: We consider the new divisor 397 and the new remainder 284, and apply the division lemma to get
397 = 284 x 1 + 113
We consider the new divisor 284 and the new remainder 113,and apply the division lemma to get
284 = 113 x 2 + 58
We consider the new divisor 113 and the new remainder 58,and apply the division lemma to get
113 = 58 x 1 + 55
We consider the new divisor 58 and the new remainder 55,and apply the division lemma to get
58 = 55 x 1 + 3
We consider the new divisor 55 and the new remainder 3,and apply the division lemma to get
55 = 3 x 18 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2269 and 7204 is 1
Notice that 1 = HCF(3,1) = HCF(55,3) = HCF(58,55) = HCF(113,58) = HCF(284,113) = HCF(397,284) = HCF(2269,397) = HCF(7204,2269) .
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Frequently Asked Questions on HCF of 2269, 7204 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 2269, 7204?
Answer: HCF of 2269, 7204 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2269, 7204 using Euclid's Algorithm?
Answer: For arbitrary numbers 2269, 7204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.