Highest Common Factor of 288, 417, 146 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 288, 417, 146 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 417, 146 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 288, 417, 146 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 288, 417, 146 is 1.
HCF(288, 417, 146) = 1
HCF of 288, 417, 146 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 288, 417, 146 is 1.
Highest Common Factor of 288,417,146 is 1
Step 1: Since 417 > 288, we apply the division lemma to 417 and 288, to get
417 = 288 x 1 + 129
Step 2: Since the reminder 288 ≠ 0, we apply division lemma to 129 and 288, to get
288 = 129 x 2 + 30
Step 3: We consider the new divisor 129 and the new remainder 30, and apply the division lemma to get
129 = 30 x 4 + 9
We consider the new divisor 30 and the new remainder 9,and apply the division lemma to get
30 = 9 x 3 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 288 and 417 is 3
Notice that 3 = HCF(9,3) = HCF(30,9) = HCF(129,30) = HCF(288,129) = HCF(417,288) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 146 > 3, we apply the division lemma to 146 and 3, to get
146 = 3 x 48 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 146 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(146,3) .
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Frequently Asked Questions on HCF of 288, 417, 146 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 288, 417, 146?
Answer: HCF of 288, 417, 146 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 417, 146 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 417, 146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.