Highest Common Factor of 272, 576, 137 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, 576, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 576, 137 is 1 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, 576, 137 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, 576, 137 is 1.
HCF(272, 576, 137) = 1
HCF of 272, 576, 137 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, 576, 137 is 1.
Highest Common Factor of 272,576,137 is 1
Step 1: Since 576 > 272, we apply the division lemma to 576 and 272, to get
576 = 272 x 2 + 32
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 32 and 272, to get
272 = 32 x 8 + 16
Step 3: 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 576 is 16
Notice that 16 = HCF(32,16) = HCF(272,32) = HCF(576,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 137 > 16, we apply the division lemma to 137 and 16, to get
137 = 16 x 8 + 9
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 9 and 16, to get
16 = 9 x 1 + 7
Step 3: We consider the new divisor 9 and the new remainder 7, and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 137 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(137,16) .
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Frequently Asked Questions on HCF of 272, 576, 137 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, 576, 137?
Answer: HCF of 272, 576, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 576, 137 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 576, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
