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 3031, 6484, 78516 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3031, 6484, 78516 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 3031, 6484, 78516 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 3031, 6484, 78516 is 1.
HCF(3031, 6484, 78516) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3031, 6484, 78516 is 1.
Step 1: Since 6484 > 3031, we apply the division lemma to 6484 and 3031, to get
6484 = 3031 x 2 + 422
Step 2: Since the reminder 3031 ≠ 0, we apply division lemma to 422 and 3031, to get
3031 = 422 x 7 + 77
Step 3: We consider the new divisor 422 and the new remainder 77, and apply the division lemma to get
422 = 77 x 5 + 37
We consider the new divisor 77 and the new remainder 37,and apply the division lemma to get
77 = 37 x 2 + 3
We consider the new divisor 37 and the new remainder 3,and apply the division lemma to get
37 = 3 x 12 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3031 and 6484 is 1
Notice that 1 = HCF(3,1) = HCF(37,3) = HCF(77,37) = HCF(422,77) = HCF(3031,422) = HCF(6484,3031) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78516 > 1, we apply the division lemma to 78516 and 1, to get
78516 = 1 x 78516 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78516 is 1
Notice that 1 = HCF(78516,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 3031, 6484, 78516?
Answer: HCF of 3031, 6484, 78516 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3031, 6484, 78516 using Euclid's Algorithm?
Answer: For arbitrary numbers 3031, 6484, 78516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.