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 2139, 2975 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2139, 2975 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 2139, 2975 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 2139, 2975 is 1.
HCF(2139, 2975) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2139, 2975 is 1.
Step 1: Since 2975 > 2139, we apply the division lemma to 2975 and 2139, to get
2975 = 2139 x 1 + 836
Step 2: Since the reminder 2139 ≠ 0, we apply division lemma to 836 and 2139, to get
2139 = 836 x 2 + 467
Step 3: We consider the new divisor 836 and the new remainder 467, and apply the division lemma to get
836 = 467 x 1 + 369
We consider the new divisor 467 and the new remainder 369,and apply the division lemma to get
467 = 369 x 1 + 98
We consider the new divisor 369 and the new remainder 98,and apply the division lemma to get
369 = 98 x 3 + 75
We consider the new divisor 98 and the new remainder 75,and apply the division lemma to get
98 = 75 x 1 + 23
We consider the new divisor 75 and the new remainder 23,and apply the division lemma to get
75 = 23 x 3 + 6
We consider the new divisor 23 and the new remainder 6,and apply the division lemma to get
23 = 6 x 3 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2139 and 2975 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(23,6) = HCF(75,23) = HCF(98,75) = HCF(369,98) = HCF(467,369) = HCF(836,467) = HCF(2139,836) = HCF(2975,2139) .
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 2139, 2975?
Answer: HCF of 2139, 2975 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2139, 2975 using Euclid's Algorithm?
Answer: For arbitrary numbers 2139, 2975 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.