Highest Common Factor of 800, 420, 513 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 800, 420, 513 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 800, 420, 513 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 800, 420, 513 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 800, 420, 513 is 1.
HCF(800, 420, 513) = 1
HCF of 800, 420, 513 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 800, 420, 513 is 1.
Highest Common Factor of 800,420,513 is 1
Step 1: Since 800 > 420, we apply the division lemma to 800 and 420, to get
800 = 420 x 1 + 380
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 380 and 420, to get
420 = 380 x 1 + 40
Step 3: We consider the new divisor 380 and the new remainder 40, and apply the division lemma to get
380 = 40 x 9 + 20
We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 800 and 420 is 20
Notice that 20 = HCF(40,20) = HCF(380,40) = HCF(420,380) = HCF(800,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 20, we apply the division lemma to 513 and 20, to get
513 = 20 x 25 + 13
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 13 and 20, to get
20 = 13 x 1 + 7
Step 3: We consider the new divisor 13 and the new remainder 7, and apply the division lemma to get
13 = 7 x 1 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 513 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(513,20) .
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Frequently Asked Questions on HCF of 800, 420, 513 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 800, 420, 513?
Answer: HCF of 800, 420, 513 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 800, 420, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 800, 420, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.