Highest Common Factor of 2051, 1603 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 2051, 1603 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 2051, 1603 is 7 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 2051, 1603 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 2051, 1603 is 7.
HCF(2051, 1603) = 7
HCF of 2051, 1603 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2051, 1603 is 7.
Highest Common Factor of 2051,1603 is 7
Step 1: Since 2051 > 1603, we apply the division lemma to 2051 and 1603, to get
2051 = 1603 x 1 + 448
Step 2: Since the reminder 1603 ≠ 0, we apply division lemma to 448 and 1603, to get
1603 = 448 x 3 + 259
Step 3: We consider the new divisor 448 and the new remainder 259, and apply the division lemma to get
448 = 259 x 1 + 189
We consider the new divisor 259 and the new remainder 189,and apply the division lemma to get
259 = 189 x 1 + 70
We consider the new divisor 189 and the new remainder 70,and apply the division lemma to get
189 = 70 x 2 + 49
We consider the new divisor 70 and the new remainder 49,and apply the division lemma to get
70 = 49 x 1 + 21
We consider the new divisor 49 and the new remainder 21,and apply the division lemma to get
49 = 21 x 2 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 2051 and 1603 is 7
Notice that 7 = HCF(21,7) = HCF(49,21) = HCF(70,49) = HCF(189,70) = HCF(259,189) = HCF(448,259) = HCF(1603,448) = HCF(2051,1603) .
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Frequently Asked Questions on HCF of 2051, 1603 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 2051, 1603?
Answer: HCF of 2051, 1603 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2051, 1603 using Euclid's Algorithm?
Answer: For arbitrary numbers 2051, 1603 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.