Highest Common Factor of 744, 7851, 5016 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 744, 7851, 5016 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 744, 7851, 5016 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 744, 7851, 5016 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 744, 7851, 5016 is 3.
HCF(744, 7851, 5016) = 3
HCF of 744, 7851, 5016 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 744, 7851, 5016 is 3.
Highest Common Factor of 744,7851,5016 is 3
Step 1: Since 7851 > 744, we apply the division lemma to 7851 and 744, to get
7851 = 744 x 10 + 411
Step 2: Since the reminder 744 ≠ 0, we apply division lemma to 411 and 744, to get
744 = 411 x 1 + 333
Step 3: We consider the new divisor 411 and the new remainder 333, and apply the division lemma to get
411 = 333 x 1 + 78
We consider the new divisor 333 and the new remainder 78,and apply the division lemma to get
333 = 78 x 4 + 21
We consider the new divisor 78 and the new remainder 21,and apply the division lemma to get
78 = 21 x 3 + 15
We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get
21 = 15 x 1 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 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 744 and 7851 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(78,21) = HCF(333,78) = HCF(411,333) = HCF(744,411) = HCF(7851,744) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 5016 > 3, we apply the division lemma to 5016 and 3, to get
5016 = 3 x 1672 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 5016 is 3
Notice that 3 = HCF(5016,3) .
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Frequently Asked Questions on HCF of 744, 7851, 5016 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 744, 7851, 5016?
Answer: HCF of 744, 7851, 5016 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 744, 7851, 5016 using Euclid's Algorithm?
Answer: For arbitrary numbers 744, 7851, 5016 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.