Highest Common Factor of 554, 300, 272 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 554, 300, 272 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 554, 300, 272 is 2 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 554, 300, 272 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 554, 300, 272 is 2.
HCF(554, 300, 272) = 2
HCF of 554, 300, 272 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 554, 300, 272 is 2.
Highest Common Factor of 554,300,272 is 2
Step 1: Since 554 > 300, we apply the division lemma to 554 and 300, to get
554 = 300 x 1 + 254
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 254 and 300, to get
300 = 254 x 1 + 46
Step 3: We consider the new divisor 254 and the new remainder 46, and apply the division lemma to get
254 = 46 x 5 + 24
We consider the new divisor 46 and the new remainder 24,and apply the division lemma to get
46 = 24 x 1 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 554 and 300 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(46,24) = HCF(254,46) = HCF(300,254) = HCF(554,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 272 > 2, we apply the division lemma to 272 and 2, to get
272 = 2 x 136 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 272 is 2
Notice that 2 = HCF(272,2) .
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Frequently Asked Questions on HCF of 554, 300, 272 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 554, 300, 272?
Answer: HCF of 554, 300, 272 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 554, 300, 272 using Euclid's Algorithm?
Answer: For arbitrary numbers 554, 300, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.