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 315, 806, 173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 806, 173 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 315, 806, 173 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 315, 806, 173 is 1.
HCF(315, 806, 173) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 315, 806, 173 is 1.
Step 1: Since 806 > 315, we apply the division lemma to 806 and 315, to get
806 = 315 x 2 + 176
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 176 and 315, to get
315 = 176 x 1 + 139
Step 3: We consider the new divisor 176 and the new remainder 139, and apply the division lemma to get
176 = 139 x 1 + 37
We consider the new divisor 139 and the new remainder 37,and apply the division lemma to get
139 = 37 x 3 + 28
We consider the new divisor 37 and the new remainder 28,and apply the division lemma to get
37 = 28 x 1 + 9
We consider the new divisor 28 and the new remainder 9,and apply the division lemma to get
28 = 9 x 3 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 315 and 806 is 1
Notice that 1 = HCF(9,1) = HCF(28,9) = HCF(37,28) = HCF(139,37) = HCF(176,139) = HCF(315,176) = HCF(806,315) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 173 > 1, we apply the division lemma to 173 and 1, to get
173 = 1 x 173 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 173 is 1
Notice that 1 = HCF(173,1) .
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 315, 806, 173?
Answer: HCF of 315, 806, 173 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 806, 173 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 806, 173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.