Highest Common Factor of 909, 45713 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 909, 45713 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 45713 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 909, 45713 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 909, 45713 is 1.
HCF(909, 45713) = 1
HCF of 909, 45713 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 909, 45713 is 1.
Highest Common Factor of 909,45713 is 1
Step 1: Since 45713 > 909, we apply the division lemma to 45713 and 909, to get
45713 = 909 x 50 + 263
Step 2: Since the reminder 909 ≠ 0, we apply division lemma to 263 and 909, to get
909 = 263 x 3 + 120
Step 3: We consider the new divisor 263 and the new remainder 120, and apply the division lemma to get
263 = 120 x 2 + 23
We consider the new divisor 120 and the new remainder 23,and apply the division lemma to get
120 = 23 x 5 + 5
We consider the new divisor 23 and the new remainder 5,and apply the division lemma to get
23 = 5 x 4 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 909 and 45713 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(120,23) = HCF(263,120) = HCF(909,263) = HCF(45713,909) .
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Frequently Asked Questions on HCF of 909, 45713 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 909, 45713?
Answer: HCF of 909, 45713 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 45713 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 45713 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.