Highest Common Factor of 660, 2909 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 660, 2909 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 2909 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 660, 2909 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 660, 2909 is 1.
HCF(660, 2909) = 1
HCF of 660, 2909 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 2909 is 1.
Highest Common Factor of 660,2909 is 1
Step 1: Since 2909 > 660, we apply the division lemma to 2909 and 660, to get
2909 = 660 x 4 + 269
Step 2: Since the reminder 660 ≠ 0, we apply division lemma to 269 and 660, to get
660 = 269 x 2 + 122
Step 3: We consider the new divisor 269 and the new remainder 122, and apply the division lemma to get
269 = 122 x 2 + 25
We consider the new divisor 122 and the new remainder 25,and apply the division lemma to get
122 = 25 x 4 + 22
We consider the new divisor 25 and the new remainder 22,and apply the division lemma to get
25 = 22 x 1 + 3
We consider the new divisor 22 and the new remainder 3,and apply the division lemma to get
22 = 3 x 7 + 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 660 and 2909 is 1
Notice that 1 = HCF(3,1) = HCF(22,3) = HCF(25,22) = HCF(122,25) = HCF(269,122) = HCF(660,269) = HCF(2909,660) .
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Frequently Asked Questions on HCF of 660, 2909 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 660, 2909?
Answer: HCF of 660, 2909 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 2909 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 2909 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.