Highest Common Factor of 2232, 8032 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 2232, 8032 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 2232, 8032 is 8 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 2232, 8032 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 2232, 8032 is 8.
HCF(2232, 8032) = 8
HCF of 2232, 8032 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2232, 8032 is 8.
Highest Common Factor of 2232,8032 is 8
Step 1: Since 8032 > 2232, we apply the division lemma to 8032 and 2232, to get
8032 = 2232 x 3 + 1336
Step 2: Since the reminder 2232 ≠ 0, we apply division lemma to 1336 and 2232, to get
2232 = 1336 x 1 + 896
Step 3: We consider the new divisor 1336 and the new remainder 896, and apply the division lemma to get
1336 = 896 x 1 + 440
We consider the new divisor 896 and the new remainder 440,and apply the division lemma to get
896 = 440 x 2 + 16
We consider the new divisor 440 and the new remainder 16,and apply the division lemma to get
440 = 16 x 27 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 2232 and 8032 is 8
Notice that 8 = HCF(16,8) = HCF(440,16) = HCF(896,440) = HCF(1336,896) = HCF(2232,1336) = HCF(8032,2232) .
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Frequently Asked Questions on HCF of 2232, 8032 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 2232, 8032?
Answer: HCF of 2232, 8032 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2232, 8032 using Euclid's Algorithm?
Answer: For arbitrary numbers 2232, 8032 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.