Highest Common Factor of 648, 6102 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 648, 6102 i.e. 54 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 6102 is 54 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 648, 6102 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 648, 6102 is 54.
HCF(648, 6102) = 54
HCF of 648, 6102 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 6102 is 54.
Highest Common Factor of 648,6102 is 54
Step 1: Since 6102 > 648, we apply the division lemma to 6102 and 648, to get
6102 = 648 x 9 + 270
Step 2: Since the reminder 648 ≠ 0, we apply division lemma to 270 and 648, to get
648 = 270 x 2 + 108
Step 3: We consider the new divisor 270 and the new remainder 108, and apply the division lemma to get
270 = 108 x 2 + 54
We consider the new divisor 108 and the new remainder 54, and apply the division lemma to get
108 = 54 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 648 and 6102 is 54
Notice that 54 = HCF(108,54) = HCF(270,108) = HCF(648,270) = HCF(6102,648) .
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Frequently Asked Questions on HCF of 648, 6102 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 648, 6102?
Answer: HCF of 648, 6102 is 54 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 6102 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 6102 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.