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 2144, 5038 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2144, 5038 is 2 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 2144, 5038 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 2144, 5038 is 2.
HCF(2144, 5038) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2144, 5038 is 2.
Step 1: Since 5038 > 2144, we apply the division lemma to 5038 and 2144, to get
5038 = 2144 x 2 + 750
Step 2: Since the reminder 2144 ≠ 0, we apply division lemma to 750 and 2144, to get
2144 = 750 x 2 + 644
Step 3: We consider the new divisor 750 and the new remainder 644, and apply the division lemma to get
750 = 644 x 1 + 106
We consider the new divisor 644 and the new remainder 106,and apply the division lemma to get
644 = 106 x 6 + 8
We consider the new divisor 106 and the new remainder 8,and apply the division lemma to get
106 = 8 x 13 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2144 and 5038 is 2
Notice that 2 = HCF(8,2) = HCF(106,8) = HCF(644,106) = HCF(750,644) = HCF(2144,750) = HCF(5038,2144) .
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 2144, 5038?
Answer: HCF of 2144, 5038 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2144, 5038 using Euclid's Algorithm?
Answer: For arbitrary numbers 2144, 5038 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.