Highest Common Factor of 223, 608 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, 608 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 223, 608 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, 608 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, 608 is 1.
HCF(223, 608) = 1
HCF of 223, 608 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, 608 is 1.
Highest Common Factor of 223,608 is 1
Step 1: Since 608 > 223, we apply the division lemma to 608 and 223, to get
608 = 223 x 2 + 162
Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 162 and 223, to get
223 = 162 x 1 + 61
Step 3: We consider the new divisor 162 and the new remainder 61, and apply the division lemma to get
162 = 61 x 2 + 40
We consider the new divisor 61 and the new remainder 40,and apply the division lemma to get
61 = 40 x 1 + 21
We consider the new divisor 40 and the new remainder 21,and apply the division lemma to get
40 = 21 x 1 + 19
We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get
21 = 19 x 1 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 223 and 608 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) = HCF(61,40) = HCF(162,61) = HCF(223,162) = HCF(608,223) .
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Frequently Asked Questions on HCF of 223, 608 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, 608?
Answer: HCF of 223, 608 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 223, 608 using Euclid's Algorithm?
Answer: For arbitrary numbers 223, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
