Highest Common Factor of 513, 7041, 2454 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, 7041, 2454 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 7041, 2454 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, 7041, 2454 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, 7041, 2454 is 3.
HCF(513, 7041, 2454) = 3
HCF of 513, 7041, 2454 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, 7041, 2454 is 3.
Highest Common Factor of 513,7041,2454 is 3
Step 1: Since 7041 > 513, we apply the division lemma to 7041 and 513, to get
7041 = 513 x 13 + 372
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 372 and 513, to get
513 = 372 x 1 + 141
Step 3: We consider the new divisor 372 and the new remainder 141, and apply the division lemma to get
372 = 141 x 2 + 90
We consider the new divisor 141 and the new remainder 90,and apply the division lemma to get
141 = 90 x 1 + 51
We consider the new divisor 90 and the new remainder 51,and apply the division lemma to get
90 = 51 x 1 + 39
We consider the new divisor 51 and the new remainder 39,and apply the division lemma to get
51 = 39 x 1 + 12
We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get
39 = 12 x 3 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 513 and 7041 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(90,51) = HCF(141,90) = HCF(372,141) = HCF(513,372) = HCF(7041,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2454 > 3, we apply the division lemma to 2454 and 3, to get
2454 = 3 x 818 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 2454 is 3
Notice that 3 = HCF(2454,3) .
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Frequently Asked Questions on HCF of 513, 7041, 2454 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, 7041, 2454?
Answer: HCF of 513, 7041, 2454 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 7041, 2454 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 7041, 2454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.