Highest Common Factor of 523, 2230 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 523, 2230 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 523, 2230 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 523, 2230 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 523, 2230 is 1.
HCF(523, 2230) = 1
HCF of 523, 2230 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 523, 2230 is 1.
Highest Common Factor of 523,2230 is 1
Step 1: Since 2230 > 523, we apply the division lemma to 2230 and 523, to get
2230 = 523 x 4 + 138
Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 138 and 523, to get
523 = 138 x 3 + 109
Step 3: We consider the new divisor 138 and the new remainder 109, and apply the division lemma to get
138 = 109 x 1 + 29
We consider the new divisor 109 and the new remainder 29,and apply the division lemma to get
109 = 29 x 3 + 22
We consider the new divisor 29 and the new remainder 22,and apply the division lemma to get
29 = 22 x 1 + 7
We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 523 and 2230 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(29,22) = HCF(109,29) = HCF(138,109) = HCF(523,138) = HCF(2230,523) .
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Frequently Asked Questions on HCF of 523, 2230 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 523, 2230?
Answer: HCF of 523, 2230 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 523, 2230 using Euclid's Algorithm?
Answer: For arbitrary numbers 523, 2230 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.