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 317, 502, 786 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 317, 502, 786 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 317, 502, 786 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 317, 502, 786 is 1.
HCF(317, 502, 786) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 317, 502, 786 is 1.
Step 1: Since 502 > 317, we apply the division lemma to 502 and 317, to get
502 = 317 x 1 + 185
Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 185 and 317, to get
317 = 185 x 1 + 132
Step 3: We consider the new divisor 185 and the new remainder 132, and apply the division lemma to get
185 = 132 x 1 + 53
We consider the new divisor 132 and the new remainder 53,and apply the division lemma to get
132 = 53 x 2 + 26
We consider the new divisor 53 and the new remainder 26,and apply the division lemma to get
53 = 26 x 2 + 1
We consider the new divisor 26 and the new remainder 1,and apply the division lemma to get
26 = 1 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 317 and 502 is 1
Notice that 1 = HCF(26,1) = HCF(53,26) = HCF(132,53) = HCF(185,132) = HCF(317,185) = HCF(502,317) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 786 > 1, we apply the division lemma to 786 and 1, to get
786 = 1 x 786 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 786 is 1
Notice that 1 = HCF(786,1) .
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 317, 502, 786?
Answer: HCF of 317, 502, 786 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 317, 502, 786 using Euclid's Algorithm?
Answer: For arbitrary numbers 317, 502, 786 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.