Highest Common Factor of 816, 513, 60 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 816, 513, 60 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 816, 513, 60 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 816, 513, 60 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 816, 513, 60 is 3.
HCF(816, 513, 60) = 3
HCF of 816, 513, 60 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 816, 513, 60 is 3.
Highest Common Factor of 816,513,60 is 3
Step 1: Since 816 > 513, we apply the division lemma to 816 and 513, to get
816 = 513 x 1 + 303
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 303 and 513, to get
513 = 303 x 1 + 210
Step 3: We consider the new divisor 303 and the new remainder 210, and apply the division lemma to get
303 = 210 x 1 + 93
We consider the new divisor 210 and the new remainder 93,and apply the division lemma to get
210 = 93 x 2 + 24
We consider the new divisor 93 and the new remainder 24,and apply the division lemma to get
93 = 24 x 3 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 816 and 513 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(93,24) = HCF(210,93) = HCF(303,210) = HCF(513,303) = HCF(816,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 3, we apply the division lemma to 60 and 3, to get
60 = 3 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 60 is 3
Notice that 3 = HCF(60,3) .
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Frequently Asked Questions on HCF of 816, 513, 60 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 816, 513, 60?
Answer: HCF of 816, 513, 60 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 816, 513, 60 using Euclid's Algorithm?
Answer: For arbitrary numbers 816, 513, 60 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.