Highest Common Factor of 510, 642 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, 642 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 642 is 6 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, 642 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, 642 is 6.
HCF(510, 642) = 6
HCF of 510, 642 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, 642 is 6.
Highest Common Factor of 510,642 is 6
Step 1: Since 642 > 510, we apply the division lemma to 642 and 510, to get
642 = 510 x 1 + 132
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 132 and 510, to get
510 = 132 x 3 + 114
Step 3: We consider the new divisor 132 and the new remainder 114, and apply the division lemma to get
132 = 114 x 1 + 18
We consider the new divisor 114 and the new remainder 18,and apply the division lemma to get
114 = 18 x 6 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 510 and 642 is 6
Notice that 6 = HCF(18,6) = HCF(114,18) = HCF(132,114) = HCF(510,132) = HCF(642,510) .
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Frequently Asked Questions on HCF of 510, 642 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, 642?
Answer: HCF of 510, 642 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 642 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 642 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.