Highest Common Factor of 354, 227, 255 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 354, 227, 255 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 354, 227, 255 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 354, 227, 255 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 354, 227, 255 is 1.
HCF(354, 227, 255) = 1
HCF of 354, 227, 255 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 354, 227, 255 is 1.
Highest Common Factor of 354,227,255 is 1
Step 1: Since 354 > 227, we apply the division lemma to 354 and 227, to get
354 = 227 x 1 + 127
Step 2: Since the reminder 227 ≠ 0, we apply division lemma to 127 and 227, to get
227 = 127 x 1 + 100
Step 3: We consider the new divisor 127 and the new remainder 100, and apply the division lemma to get
127 = 100 x 1 + 27
We consider the new divisor 100 and the new remainder 27,and apply the division lemma to get
100 = 27 x 3 + 19
We consider the new divisor 27 and the new remainder 19,and apply the division lemma to get
27 = 19 x 1 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 354 and 227 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(27,19) = HCF(100,27) = HCF(127,100) = HCF(227,127) = HCF(354,227) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 255 > 1, we apply the division lemma to 255 and 1, to get
255 = 1 x 255 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 255 is 1
Notice that 1 = HCF(255,1) .
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Frequently Asked Questions on HCF of 354, 227, 255 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 354, 227, 255?
Answer: HCF of 354, 227, 255 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 354, 227, 255 using Euclid's Algorithm?
Answer: For arbitrary numbers 354, 227, 255 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.