Highest Common Factor of 640, 504, 109 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, 504, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 504, 109 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, 504, 109 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, 504, 109 is 1.
HCF(640, 504, 109) = 1
HCF of 640, 504, 109 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, 504, 109 is 1.
Highest Common Factor of 640,504,109 is 1
Step 1: Since 640 > 504, we apply the division lemma to 640 and 504, to get
640 = 504 x 1 + 136
Step 2: Since the reminder 504 ≠ 0, we apply division lemma to 136 and 504, to get
504 = 136 x 3 + 96
Step 3: We consider the new divisor 136 and the new remainder 96, and apply the division lemma to get
136 = 96 x 1 + 40
We consider the new divisor 96 and the new remainder 40,and apply the division lemma to get
96 = 40 x 2 + 16
We consider the new divisor 40 and the new remainder 16,and apply the division lemma to get
40 = 16 x 2 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 640 and 504 is 8
Notice that 8 = HCF(16,8) = HCF(40,16) = HCF(96,40) = HCF(136,96) = HCF(504,136) = HCF(640,504) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 8, we apply the division lemma to 109 and 8, to get
109 = 8 x 13 + 5
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 5 and 8, to get
8 = 5 x 1 + 3
Step 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 8 and 109 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(109,8) .
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Frequently Asked Questions on HCF of 640, 504, 109 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, 504, 109?
Answer: HCF of 640, 504, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 504, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 504, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.