Highest Common Factor of 1632, 7005 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 1632, 7005 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 1632, 7005 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 1632, 7005 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 1632, 7005 is 3.
HCF(1632, 7005) = 3
HCF of 1632, 7005 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1632, 7005 is 3.
Highest Common Factor of 1632,7005 is 3
Step 1: Since 7005 > 1632, we apply the division lemma to 7005 and 1632, to get
7005 = 1632 x 4 + 477
Step 2: Since the reminder 1632 ≠ 0, we apply division lemma to 477 and 1632, to get
1632 = 477 x 3 + 201
Step 3: We consider the new divisor 477 and the new remainder 201, and apply the division lemma to get
477 = 201 x 2 + 75
We consider the new divisor 201 and the new remainder 75,and apply the division lemma to get
201 = 75 x 2 + 51
We consider the new divisor 75 and the new remainder 51,and apply the division lemma to get
75 = 51 x 1 + 24
We consider the new divisor 51 and the new remainder 24,and apply the division lemma to get
51 = 24 x 2 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 1632 and 7005 is 3
Notice that 3 = HCF(24,3) = HCF(51,24) = HCF(75,51) = HCF(201,75) = HCF(477,201) = HCF(1632,477) = HCF(7005,1632) .
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Frequently Asked Questions on HCF of 1632, 7005 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 1632, 7005?
Answer: HCF of 1632, 7005 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1632, 7005 using Euclid's Algorithm?
Answer: For arbitrary numbers 1632, 7005 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
