Highest Common Factor of 2199, 1905 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 2199, 1905 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2199, 1905 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 2199, 1905 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 2199, 1905 is 3.
HCF(2199, 1905) = 3
HCF of 2199, 1905 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2199, 1905 is 3.
Highest Common Factor of 2199,1905 is 3
Step 1: Since 2199 > 1905, we apply the division lemma to 2199 and 1905, to get
2199 = 1905 x 1 + 294
Step 2: Since the reminder 1905 ≠ 0, we apply division lemma to 294 and 1905, to get
1905 = 294 x 6 + 141
Step 3: We consider the new divisor 294 and the new remainder 141, and apply the division lemma to get
294 = 141 x 2 + 12
We consider the new divisor 141 and the new remainder 12,and apply the division lemma to get
141 = 12 x 11 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2199 and 1905 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(141,12) = HCF(294,141) = HCF(1905,294) = HCF(2199,1905) .
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Frequently Asked Questions on HCF of 2199, 1905 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 2199, 1905?
Answer: HCF of 2199, 1905 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2199, 1905 using Euclid's Algorithm?
Answer: For arbitrary numbers 2199, 1905 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.