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 3051, 2140 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3051, 2140 is 1 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 3051, 2140 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 3051, 2140 is 1.
HCF(3051, 2140) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3051, 2140 is 1.
Step 1: Since 3051 > 2140, we apply the division lemma to 3051 and 2140, to get
3051 = 2140 x 1 + 911
Step 2: Since the reminder 2140 ≠ 0, we apply division lemma to 911 and 2140, to get
2140 = 911 x 2 + 318
Step 3: We consider the new divisor 911 and the new remainder 318, and apply the division lemma to get
911 = 318 x 2 + 275
We consider the new divisor 318 and the new remainder 275,and apply the division lemma to get
318 = 275 x 1 + 43
We consider the new divisor 275 and the new remainder 43,and apply the division lemma to get
275 = 43 x 6 + 17
We consider the new divisor 43 and the new remainder 17,and apply the division lemma to get
43 = 17 x 2 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3051 and 2140 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(43,17) = HCF(275,43) = HCF(318,275) = HCF(911,318) = HCF(2140,911) = HCF(3051,2140) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 3051, 2140?
Answer: HCF of 3051, 2140 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3051, 2140 using Euclid's Algorithm?
Answer: For arbitrary numbers 3051, 2140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.