Highest Common Factor of 2312, 5532 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 2312, 5532 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2312, 5532 is 4 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 2312, 5532 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 2312, 5532 is 4.
HCF(2312, 5532) = 4
HCF of 2312, 5532 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2312, 5532 is 4.
Highest Common Factor of 2312,5532 is 4
Step 1: Since 5532 > 2312, we apply the division lemma to 5532 and 2312, to get
5532 = 2312 x 2 + 908
Step 2: Since the reminder 2312 ≠ 0, we apply division lemma to 908 and 2312, to get
2312 = 908 x 2 + 496
Step 3: We consider the new divisor 908 and the new remainder 496, and apply the division lemma to get
908 = 496 x 1 + 412
We consider the new divisor 496 and the new remainder 412,and apply the division lemma to get
496 = 412 x 1 + 84
We consider the new divisor 412 and the new remainder 84,and apply the division lemma to get
412 = 84 x 4 + 76
We consider the new divisor 84 and the new remainder 76,and apply the division lemma to get
84 = 76 x 1 + 8
We consider the new divisor 76 and the new remainder 8,and apply the division lemma to get
76 = 8 x 9 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2312 and 5532 is 4
Notice that 4 = HCF(8,4) = HCF(76,8) = HCF(84,76) = HCF(412,84) = HCF(496,412) = HCF(908,496) = HCF(2312,908) = HCF(5532,2312) .
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Frequently Asked Questions on HCF of 2312, 5532 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 2312, 5532?
Answer: HCF of 2312, 5532 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2312, 5532 using Euclid's Algorithm?
Answer: For arbitrary numbers 2312, 5532 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.