Highest Common Factor of 528, 6705 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 528, 6705 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 528, 6705 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 528, 6705 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 528, 6705 is 3.
HCF(528, 6705) = 3
HCF of 528, 6705 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 528, 6705 is 3.
Highest Common Factor of 528,6705 is 3
Step 1: Since 6705 > 528, we apply the division lemma to 6705 and 528, to get
6705 = 528 x 12 + 369
Step 2: Since the reminder 528 ≠ 0, we apply division lemma to 369 and 528, to get
528 = 369 x 1 + 159
Step 3: We consider the new divisor 369 and the new remainder 159, and apply the division lemma to get
369 = 159 x 2 + 51
We consider the new divisor 159 and the new remainder 51,and apply the division lemma to get
159 = 51 x 3 + 6
We consider the new divisor 51 and the new remainder 6,and apply the division lemma to get
51 = 6 x 8 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma 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 528 and 6705 is 3
Notice that 3 = HCF(6,3) = HCF(51,6) = HCF(159,51) = HCF(369,159) = HCF(528,369) = HCF(6705,528) .
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Frequently Asked Questions on HCF of 528, 6705 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 528, 6705?
Answer: HCF of 528, 6705 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 528, 6705 using Euclid's Algorithm?
Answer: For arbitrary numbers 528, 6705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.