Highest Common Factor of 2112, 4365 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 2112, 4365 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2112, 4365 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 2112, 4365 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 2112, 4365 is 3.
HCF(2112, 4365) = 3
HCF of 2112, 4365 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2112, 4365 is 3.
Highest Common Factor of 2112,4365 is 3
Step 1: Since 4365 > 2112, we apply the division lemma to 4365 and 2112, to get
4365 = 2112 x 2 + 141
Step 2: Since the reminder 2112 ≠ 0, we apply division lemma to 141 and 2112, to get
2112 = 141 x 14 + 138
Step 3: We consider the new divisor 141 and the new remainder 138, and apply the division lemma to get
141 = 138 x 1 + 3
We consider the new divisor 138 and the new remainder 3, and apply the division lemma to get
138 = 3 x 46 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2112 and 4365 is 3
Notice that 3 = HCF(138,3) = HCF(141,138) = HCF(2112,141) = HCF(4365,2112) .
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Frequently Asked Questions on HCF of 2112, 4365 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 2112, 4365?
Answer: HCF of 2112, 4365 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2112, 4365 using Euclid's Algorithm?
Answer: For arbitrary numbers 2112, 4365 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.