Highest Common Factor of 640, 240, 291 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 640, 240, 291 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 240, 291 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 640, 240, 291 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 640, 240, 291 is 1.
HCF(640, 240, 291) = 1
HCF of 640, 240, 291 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 640, 240, 291 is 1.
Highest Common Factor of 640,240,291 is 1
Step 1: Since 640 > 240, we apply the division lemma to 640 and 240, to get
640 = 240 x 2 + 160
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 160 and 240, to get
240 = 160 x 1 + 80
Step 3: We consider the new divisor 160 and the new remainder 80, and apply the division lemma to get
160 = 80 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 80, the HCF of 640 and 240 is 80
Notice that 80 = HCF(160,80) = HCF(240,160) = HCF(640,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 291 > 80, we apply the division lemma to 291 and 80, to get
291 = 80 x 3 + 51
Step 2: Since the reminder 80 ≠ 0, we apply division lemma to 51 and 80, to get
80 = 51 x 1 + 29
Step 3: We consider the new divisor 51 and the new remainder 29, and apply the division lemma to get
51 = 29 x 1 + 22
We consider the new divisor 29 and the new remainder 22,and apply the division lemma to get
29 = 22 x 1 + 7
We consider the new divisor 22 and the new remainder 7,and apply the division lemma to get
22 = 7 x 3 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 80 and 291 is 1
Notice that 1 = HCF(7,1) = HCF(22,7) = HCF(29,22) = HCF(51,29) = HCF(80,51) = HCF(291,80) .
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Frequently Asked Questions on HCF of 640, 240, 291 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 640, 240, 291?
Answer: HCF of 640, 240, 291 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 240, 291 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 240, 291 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.