Highest Common Factor of 516, 654, 758 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 516, 654, 758 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 516, 654, 758 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 516, 654, 758 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 516, 654, 758 is 2.
HCF(516, 654, 758) = 2
HCF of 516, 654, 758 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 516, 654, 758 is 2.
Highest Common Factor of 516,654,758 is 2
Step 1: Since 654 > 516, we apply the division lemma to 654 and 516, to get
654 = 516 x 1 + 138
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 138 and 516, to get
516 = 138 x 3 + 102
Step 3: We consider the new divisor 138 and the new remainder 102, and apply the division lemma to get
138 = 102 x 1 + 36
We consider the new divisor 102 and the new remainder 36,and apply the division lemma to get
102 = 36 x 2 + 30
We consider the new divisor 36 and the new remainder 30,and apply the division lemma to get
36 = 30 x 1 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 516 and 654 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(102,36) = HCF(138,102) = HCF(516,138) = HCF(654,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 758 > 6, we apply the division lemma to 758 and 6, to get
758 = 6 x 126 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 758 is 2
Notice that 2 = HCF(6,2) = HCF(758,6) .
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Frequently Asked Questions on HCF of 516, 654, 758 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 516, 654, 758?
Answer: HCF of 516, 654, 758 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 516, 654, 758 using Euclid's Algorithm?
Answer: For arbitrary numbers 516, 654, 758 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.