Highest Common Factor of 272, 1032 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 272, 1032 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 1032 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 272, 1032 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 272, 1032 is 8.
HCF(272, 1032) = 8
HCF of 272, 1032 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 272, 1032 is 8.
Highest Common Factor of 272,1032 is 8
Step 1: Since 1032 > 272, we apply the division lemma to 1032 and 272, to get
1032 = 272 x 3 + 216
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 216 and 272, to get
272 = 216 x 1 + 56
Step 3: We consider the new divisor 216 and the new remainder 56, and apply the division lemma to get
216 = 56 x 3 + 48
We consider the new divisor 56 and the new remainder 48,and apply the division lemma to get
56 = 48 x 1 + 8
We consider the new divisor 48 and the new remainder 8,and apply the division lemma to get
48 = 8 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 272 and 1032 is 8
Notice that 8 = HCF(48,8) = HCF(56,48) = HCF(216,56) = HCF(272,216) = HCF(1032,272) .
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Frequently Asked Questions on HCF of 272, 1032 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 272, 1032?
Answer: HCF of 272, 1032 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 1032 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 1032 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.