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 8375, 7130, 75063 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8375, 7130, 75063 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 8375, 7130, 75063 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 8375, 7130, 75063 is 1.
HCF(8375, 7130, 75063) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8375, 7130, 75063 is 1.
Step 1: Since 8375 > 7130, we apply the division lemma to 8375 and 7130, to get
8375 = 7130 x 1 + 1245
Step 2: Since the reminder 7130 ≠ 0, we apply division lemma to 1245 and 7130, to get
7130 = 1245 x 5 + 905
Step 3: We consider the new divisor 1245 and the new remainder 905, and apply the division lemma to get
1245 = 905 x 1 + 340
We consider the new divisor 905 and the new remainder 340,and apply the division lemma to get
905 = 340 x 2 + 225
We consider the new divisor 340 and the new remainder 225,and apply the division lemma to get
340 = 225 x 1 + 115
We consider the new divisor 225 and the new remainder 115,and apply the division lemma to get
225 = 115 x 1 + 110
We consider the new divisor 115 and the new remainder 110,and apply the division lemma to get
115 = 110 x 1 + 5
We consider the new divisor 110 and the new remainder 5,and apply the division lemma to get
110 = 5 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 8375 and 7130 is 5
Notice that 5 = HCF(110,5) = HCF(115,110) = HCF(225,115) = HCF(340,225) = HCF(905,340) = HCF(1245,905) = HCF(7130,1245) = HCF(8375,7130) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 75063 > 5, we apply the division lemma to 75063 and 5, to get
75063 = 5 x 15012 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 75063 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(75063,5) .
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 8375, 7130, 75063?
Answer: HCF of 8375, 7130, 75063 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8375, 7130, 75063 using Euclid's Algorithm?
Answer: For arbitrary numbers 8375, 7130, 75063 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.