Highest Common Factor of 510, 648, 135 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 510, 648, 135 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 648, 135 is 3 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 510, 648, 135 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 510, 648, 135 is 3.
HCF(510, 648, 135) = 3
HCF of 510, 648, 135 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 648, 135 is 3.
Highest Common Factor of 510,648,135 is 3
Step 1: Since 648 > 510, we apply the division lemma to 648 and 510, to get
648 = 510 x 1 + 138
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 138 and 510, to get
510 = 138 x 3 + 96
Step 3: We consider the new divisor 138 and the new remainder 96, and apply the division lemma to get
138 = 96 x 1 + 42
We consider the new divisor 96 and the new remainder 42,and apply the division lemma to get
96 = 42 x 2 + 12
We consider the new divisor 42 and the new remainder 12,and apply the division lemma to get
42 = 12 x 3 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 510 and 648 is 6
Notice that 6 = HCF(12,6) = HCF(42,12) = HCF(96,42) = HCF(138,96) = HCF(510,138) = HCF(648,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 135 > 6, we apply the division lemma to 135 and 6, to get
135 = 6 x 22 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 135 is 3
Notice that 3 = HCF(6,3) = HCF(135,6) .
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Frequently Asked Questions on HCF of 510, 648, 135 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 510, 648, 135?
Answer: HCF of 510, 648, 135 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 648, 135 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 648, 135 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.