Highest Common Factor of 913, 585 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 913, 585 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 913, 585 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 913, 585 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 913, 585 is 1.
HCF(913, 585) = 1
HCF of 913, 585 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 913, 585 is 1.
Highest Common Factor of 913,585 is 1
Step 1: Since 913 > 585, we apply the division lemma to 913 and 585, to get
913 = 585 x 1 + 328
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 328 and 585, to get
585 = 328 x 1 + 257
Step 3: We consider the new divisor 328 and the new remainder 257, and apply the division lemma to get
328 = 257 x 1 + 71
We consider the new divisor 257 and the new remainder 71,and apply the division lemma to get
257 = 71 x 3 + 44
We consider the new divisor 71 and the new remainder 44,and apply the division lemma to get
71 = 44 x 1 + 27
We consider the new divisor 44 and the new remainder 27,and apply the division lemma to get
44 = 27 x 1 + 17
We consider the new divisor 27 and the new remainder 17,and apply the division lemma to get
27 = 17 x 1 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 913 and 585 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(44,27) = HCF(71,44) = HCF(257,71) = HCF(328,257) = HCF(585,328) = HCF(913,585) .
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Frequently Asked Questions on HCF of 913, 585 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 913, 585?
Answer: HCF of 913, 585 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 913, 585 using Euclid's Algorithm?
Answer: For arbitrary numbers 913, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.