Highest Common Factor of 317, 560 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, 560 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 317, 560 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, 560 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, 560 is 1.
HCF(317, 560) = 1
HCF of 317, 560 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, 560 is 1.
Highest Common Factor of 317,560 is 1
Step 1: Since 560 > 317, we apply the division lemma to 560 and 317, to get
560 = 317 x 1 + 243
Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 243 and 317, to get
317 = 243 x 1 + 74
Step 3: We consider the new divisor 243 and the new remainder 74, and apply the division lemma to get
243 = 74 x 3 + 21
We consider the new divisor 74 and the new remainder 21,and apply the division lemma to get
74 = 21 x 3 + 11
We consider the new divisor 21 and the new remainder 11,and apply the division lemma to get
21 = 11 x 1 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 317 and 560 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(21,11) = HCF(74,21) = HCF(243,74) = HCF(317,243) = HCF(560,317) .
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Frequently Asked Questions on HCF of 317, 560 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, 560?
Answer: HCF of 317, 560 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 317, 560 using Euclid's Algorithm?
Answer: For arbitrary numbers 317, 560 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.