Highest Common Factor of 8712, 3525 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 8712, 3525 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8712, 3525 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 8712, 3525 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 8712, 3525 is 3.
HCF(8712, 3525) = 3
HCF of 8712, 3525 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8712, 3525 is 3.
Highest Common Factor of 8712,3525 is 3
Step 1: Since 8712 > 3525, we apply the division lemma to 8712 and 3525, to get
8712 = 3525 x 2 + 1662
Step 2: Since the reminder 3525 ≠ 0, we apply division lemma to 1662 and 3525, to get
3525 = 1662 x 2 + 201
Step 3: We consider the new divisor 1662 and the new remainder 201, and apply the division lemma to get
1662 = 201 x 8 + 54
We consider the new divisor 201 and the new remainder 54,and apply the division lemma to get
201 = 54 x 3 + 39
We consider the new divisor 54 and the new remainder 39,and apply the division lemma to get
54 = 39 x 1 + 15
We consider the new divisor 39 and the new remainder 15,and apply the division lemma to get
39 = 15 x 2 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 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 8712 and 3525 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(39,15) = HCF(54,39) = HCF(201,54) = HCF(1662,201) = HCF(3525,1662) = HCF(8712,3525) .
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Frequently Asked Questions on HCF of 8712, 3525 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 8712, 3525?
Answer: HCF of 8712, 3525 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8712, 3525 using Euclid's Algorithm?
Answer: For arbitrary numbers 8712, 3525 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.