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 4015, 6495, 71108 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4015, 6495, 71108 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 4015, 6495, 71108 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 4015, 6495, 71108 is 1.
HCF(4015, 6495, 71108) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4015, 6495, 71108 is 1.
Step 1: Since 6495 > 4015, we apply the division lemma to 6495 and 4015, to get
6495 = 4015 x 1 + 2480
Step 2: Since the reminder 4015 ≠ 0, we apply division lemma to 2480 and 4015, to get
4015 = 2480 x 1 + 1535
Step 3: We consider the new divisor 2480 and the new remainder 1535, and apply the division lemma to get
2480 = 1535 x 1 + 945
We consider the new divisor 1535 and the new remainder 945,and apply the division lemma to get
1535 = 945 x 1 + 590
We consider the new divisor 945 and the new remainder 590,and apply the division lemma to get
945 = 590 x 1 + 355
We consider the new divisor 590 and the new remainder 355,and apply the division lemma to get
590 = 355 x 1 + 235
We consider the new divisor 355 and the new remainder 235,and apply the division lemma to get
355 = 235 x 1 + 120
We consider the new divisor 235 and the new remainder 120,and apply the division lemma to get
235 = 120 x 1 + 115
We consider the new divisor 120 and the new remainder 115,and apply the division lemma to get
120 = 115 x 1 + 5
We consider the new divisor 115 and the new remainder 5,and apply the division lemma to get
115 = 5 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 4015 and 6495 is 5
Notice that 5 = HCF(115,5) = HCF(120,115) = HCF(235,120) = HCF(355,235) = HCF(590,355) = HCF(945,590) = HCF(1535,945) = HCF(2480,1535) = HCF(4015,2480) = HCF(6495,4015) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 71108 > 5, we apply the division lemma to 71108 and 5, to get
71108 = 5 x 14221 + 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 71108 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(71108,5) .
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 4015, 6495, 71108?
Answer: HCF of 4015, 6495, 71108 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4015, 6495, 71108 using Euclid's Algorithm?
Answer: For arbitrary numbers 4015, 6495, 71108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.