Highest Common Factor of 45, 204, 351 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 45, 204, 351 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 45, 204, 351 is 3 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 45, 204, 351 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 45, 204, 351 is 3.
HCF(45, 204, 351) = 3
HCF of 45, 204, 351 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 45, 204, 351 is 3.
Highest Common Factor of 45,204,351 is 3
Step 1: Since 204 > 45, we apply the division lemma to 204 and 45, to get
204 = 45 x 4 + 24
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 24 and 45, to get
45 = 24 x 1 + 21
Step 3: We consider the new divisor 24 and the new remainder 21, and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3, and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 45 and 204 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(204,45) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 351 > 3, we apply the division lemma to 351 and 3, to get
351 = 3 x 117 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 351 is 3
Notice that 3 = HCF(351,3) .
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Frequently Asked Questions on HCF of 45, 204, 351 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 45, 204, 351?
Answer: HCF of 45, 204, 351 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 45, 204, 351 using Euclid's Algorithm?
Answer: For arbitrary numbers 45, 204, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.