Highest Common Factor of 640, 526, 310 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, 526, 310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 640, 526, 310 is 2 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, 526, 310 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, 526, 310 is 2.
HCF(640, 526, 310) = 2
HCF of 640, 526, 310 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, 526, 310 is 2.
Highest Common Factor of 640,526,310 is 2
Step 1: Since 640 > 526, we apply the division lemma to 640 and 526, to get
640 = 526 x 1 + 114
Step 2: Since the reminder 526 ≠ 0, we apply division lemma to 114 and 526, to get
526 = 114 x 4 + 70
Step 3: We consider the new divisor 114 and the new remainder 70, and apply the division lemma to get
114 = 70 x 1 + 44
We consider the new divisor 70 and the new remainder 44,and apply the division lemma to get
70 = 44 x 1 + 26
We consider the new divisor 44 and the new remainder 26,and apply the division lemma to get
44 = 26 x 1 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 640 and 526 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(44,26) = HCF(70,44) = HCF(114,70) = HCF(526,114) = HCF(640,526) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 310 > 2, we apply the division lemma to 310 and 2, to get
310 = 2 x 155 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 310 is 2
Notice that 2 = HCF(310,2) .
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Frequently Asked Questions on HCF of 640, 526, 310 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, 526, 310?
Answer: HCF of 640, 526, 310 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 640, 526, 310 using Euclid's Algorithm?
Answer: For arbitrary numbers 640, 526, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.