Highest Common Factor of 269, 640 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 269, 640 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 269, 640 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 269, 640 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 269, 640 is 1.
HCF(269, 640) = 1
HCF of 269, 640 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 269, 640 is 1.
Highest Common Factor of 269,640 is 1
Step 1: Since 640 > 269, we apply the division lemma to 640 and 269, to get
640 = 269 x 2 + 102
Step 2: Since the reminder 269 ≠ 0, we apply division lemma to 102 and 269, to get
269 = 102 x 2 + 65
Step 3: We consider the new divisor 102 and the new remainder 65, and apply the division lemma to get
102 = 65 x 1 + 37
We consider the new divisor 65 and the new remainder 37,and apply the division lemma to get
65 = 37 x 1 + 28
We consider the new divisor 37 and the new remainder 28,and apply the division lemma to get
37 = 28 x 1 + 9
We consider the new divisor 28 and the new remainder 9,and apply the division lemma to get
28 = 9 x 3 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 269 and 640 is 1
Notice that 1 = HCF(9,1) = HCF(28,9) = HCF(37,28) = HCF(65,37) = HCF(102,65) = HCF(269,102) = HCF(640,269) .
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Frequently Asked Questions on HCF of 269, 640 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 269, 640?
Answer: HCF of 269, 640 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 269, 640 using Euclid's Algorithm?
Answer: For arbitrary numbers 269, 640 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.