Highest Common Factor of 317, 825 using Euclid's algorithm
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, 825 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 317, 825 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, 825 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, 825 is 1.
HCF(317, 825) = 1
HCF of 317, 825 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 317, 825 is 1.
Highest Common Factor of 317,825 is 1
Step 1: Since 825 > 317, we apply the division lemma to 825 and 317, to get
825 = 317 x 2 + 191
Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 191 and 317, to get
317 = 191 x 1 + 126
Step 3: We consider the new divisor 191 and the new remainder 126, and apply the division lemma to get
191 = 126 x 1 + 65
We consider the new divisor 126 and the new remainder 65,and apply the division lemma to get
126 = 65 x 1 + 61
We consider the new divisor 65 and the new remainder 61,and apply the division lemma to get
65 = 61 x 1 + 4
We consider the new divisor 61 and the new remainder 4,and apply the division lemma to get
61 = 4 x 15 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 317 and 825 is 1
Notice that 1 = HCF(4,1) = HCF(61,4) = HCF(65,61) = HCF(126,65) = HCF(191,126) = HCF(317,191) = HCF(825,317) .
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Frequently Asked Questions on HCF of 317, 825 using Euclid's Algorithm
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, 825?
Answer: HCF of 317, 825 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 317, 825 using Euclid's Algorithm?
Answer: For arbitrary numbers 317, 825 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.