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 3713, 8426, 54124 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3713, 8426, 54124 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 3713, 8426, 54124 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 3713, 8426, 54124 is 1.
HCF(3713, 8426, 54124) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3713, 8426, 54124 is 1.
Step 1: Since 8426 > 3713, we apply the division lemma to 8426 and 3713, to get
8426 = 3713 x 2 + 1000
Step 2: Since the reminder 3713 ≠ 0, we apply division lemma to 1000 and 3713, to get
3713 = 1000 x 3 + 713
Step 3: We consider the new divisor 1000 and the new remainder 713, and apply the division lemma to get
1000 = 713 x 1 + 287
We consider the new divisor 713 and the new remainder 287,and apply the division lemma to get
713 = 287 x 2 + 139
We consider the new divisor 287 and the new remainder 139,and apply the division lemma to get
287 = 139 x 2 + 9
We consider the new divisor 139 and the new remainder 9,and apply the division lemma to get
139 = 9 x 15 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3713 and 8426 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(139,9) = HCF(287,139) = HCF(713,287) = HCF(1000,713) = HCF(3713,1000) = HCF(8426,3713) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54124 > 1, we apply the division lemma to 54124 and 1, to get
54124 = 1 x 54124 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54124 is 1
Notice that 1 = HCF(54124,1) .
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 3713, 8426, 54124?
Answer: HCF of 3713, 8426, 54124 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3713, 8426, 54124 using Euclid's Algorithm?
Answer: For arbitrary numbers 3713, 8426, 54124 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.