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 1306, 8177, 47051 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1306, 8177, 47051 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 1306, 8177, 47051 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 1306, 8177, 47051 is 1.
HCF(1306, 8177, 47051) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1306, 8177, 47051 is 1.
Step 1: Since 8177 > 1306, we apply the division lemma to 8177 and 1306, to get
8177 = 1306 x 6 + 341
Step 2: Since the reminder 1306 ≠ 0, we apply division lemma to 341 and 1306, to get
1306 = 341 x 3 + 283
Step 3: We consider the new divisor 341 and the new remainder 283, and apply the division lemma to get
341 = 283 x 1 + 58
We consider the new divisor 283 and the new remainder 58,and apply the division lemma to get
283 = 58 x 4 + 51
We consider the new divisor 58 and the new remainder 51,and apply the division lemma to get
58 = 51 x 1 + 7
We consider the new divisor 51 and the new remainder 7,and apply the division lemma to get
51 = 7 x 7 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 1306 and 8177 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(51,7) = HCF(58,51) = HCF(283,58) = HCF(341,283) = HCF(1306,341) = HCF(8177,1306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 47051 > 1, we apply the division lemma to 47051 and 1, to get
47051 = 1 x 47051 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 47051 is 1
Notice that 1 = HCF(47051,1) .
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 1306, 8177, 47051?
Answer: HCF of 1306, 8177, 47051 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1306, 8177, 47051 using Euclid's Algorithm?
Answer: For arbitrary numbers 1306, 8177, 47051 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.