Highest Common Factor of 272, 17632 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, 17632 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 17632 is 16 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, 17632 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, 17632 is 16.
HCF(272, 17632) = 16
HCF of 272, 17632 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, 17632 is 16.
Highest Common Factor of 272,17632 is 16
Step 1: Since 17632 > 272, we apply the division lemma to 17632 and 272, to get
17632 = 272 x 64 + 224
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 224 and 272, to get
272 = 224 x 1 + 48
Step 3: We consider the new divisor 224 and the new remainder 48, and apply the division lemma to get
224 = 48 x 4 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 272 and 17632 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(224,48) = HCF(272,224) = HCF(17632,272) .
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Frequently Asked Questions on HCF of 272, 17632 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, 17632?
Answer: HCF of 272, 17632 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 17632 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 17632 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.