Highest Common Factor of 513, 743, 222 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 513, 743, 222 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 743, 222 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 513, 743, 222 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 513, 743, 222 is 1.
HCF(513, 743, 222) = 1
HCF of 513, 743, 222 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 743, 222 is 1.
Highest Common Factor of 513,743,222 is 1
Step 1: Since 743 > 513, we apply the division lemma to 743 and 513, to get
743 = 513 x 1 + 230
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 230 and 513, to get
513 = 230 x 2 + 53
Step 3: We consider the new divisor 230 and the new remainder 53, and apply the division lemma to get
230 = 53 x 4 + 18
We consider the new divisor 53 and the new remainder 18,and apply the division lemma to get
53 = 18 x 2 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 513 and 743 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(53,18) = HCF(230,53) = HCF(513,230) = HCF(743,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 222 > 1, we apply the division lemma to 222 and 1, to get
222 = 1 x 222 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 222 is 1
Notice that 1 = HCF(222,1) .
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Frequently Asked Questions on HCF of 513, 743, 222 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 513, 743, 222?
Answer: HCF of 513, 743, 222 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 743, 222 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 743, 222 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.