Highest Common Factor of 513, 741, 993 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, 741, 993 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 741, 993 is 3 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, 741, 993 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, 741, 993 is 3.
HCF(513, 741, 993) = 3
HCF of 513, 741, 993 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, 741, 993 is 3.
Highest Common Factor of 513,741,993 is 3
Step 1: Since 741 > 513, we apply the division lemma to 741 and 513, to get
741 = 513 x 1 + 228
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 228 and 513, to get
513 = 228 x 2 + 57
Step 3: We consider the new divisor 228 and the new remainder 57, and apply the division lemma to get
228 = 57 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 57, the HCF of 513 and 741 is 57
Notice that 57 = HCF(228,57) = HCF(513,228) = HCF(741,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 993 > 57, we apply the division lemma to 993 and 57, to get
993 = 57 x 17 + 24
Step 2: Since the reminder 57 ≠ 0, we apply division lemma to 24 and 57, to get
57 = 24 x 2 + 9
Step 3: We consider the new divisor 24 and the new remainder 9, and apply the division lemma to get
24 = 9 x 2 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 57 and 993 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(24,9) = HCF(57,24) = HCF(993,57) .
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Frequently Asked Questions on HCF of 513, 741, 993 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, 741, 993?
Answer: HCF of 513, 741, 993 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 741, 993 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 741, 993 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.