Highest Common Factor of 223, 565 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 223, 565 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 223, 565 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 223, 565 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 223, 565 is 1.
HCF(223, 565) = 1
HCF of 223, 565 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 223, 565 is 1.
Highest Common Factor of 223,565 is 1
Step 1: Since 565 > 223, we apply the division lemma to 565 and 223, to get
565 = 223 x 2 + 119
Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 119 and 223, to get
223 = 119 x 1 + 104
Step 3: We consider the new divisor 119 and the new remainder 104, and apply the division lemma to get
119 = 104 x 1 + 15
We consider the new divisor 104 and the new remainder 15,and apply the division lemma to get
104 = 15 x 6 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 223 and 565 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(104,15) = HCF(119,104) = HCF(223,119) = HCF(565,223) .
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Frequently Asked Questions on HCF of 223, 565 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 223, 565?
Answer: HCF of 223, 565 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 223, 565 using Euclid's Algorithm?
Answer: For arbitrary numbers 223, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.