Highest Common Factor of 2144, 3232 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 2144, 3232 i.e. 32 the largest integer that leaves a remainder zero for all numbers.
HCF of 2144, 3232 is 32 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, 3232 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, 3232 is 32.
HCF(2144, 3232) = 32
HCF of 2144, 3232 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2144, 3232 is 32.
Highest Common Factor of 2144,3232 is 32
Step 1: Since 3232 > 2144, we apply the division lemma to 3232 and 2144, to get
3232 = 2144 x 1 + 1088
Step 2: Since the reminder 2144 ≠ 0, we apply division lemma to 1088 and 2144, to get
2144 = 1088 x 1 + 1056
Step 3: We consider the new divisor 1088 and the new remainder 1056, and apply the division lemma to get
1088 = 1056 x 1 + 32
We consider the new divisor 1056 and the new remainder 32, and apply the division lemma to get
1056 = 32 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 2144 and 3232 is 32
Notice that 32 = HCF(1056,32) = HCF(1088,1056) = HCF(2144,1088) = HCF(3232,2144) .
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Frequently Asked Questions on HCF of 2144, 3232 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 2144, 3232?
Answer: HCF of 2144, 3232 is 32 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2144, 3232 using Euclid's Algorithm?
Answer: For arbitrary numbers 2144, 3232 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.