Highest Common Factor of 141, 204, 330 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 141, 204, 330 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 141, 204, 330 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 141, 204, 330 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 141, 204, 330 is 3.
HCF(141, 204, 330) = 3
HCF of 141, 204, 330 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 141, 204, 330 is 3.
Highest Common Factor of 141,204,330 is 3
Step 1: Since 204 > 141, we apply the division lemma to 204 and 141, to get
204 = 141 x 1 + 63
Step 2: Since the reminder 141 ≠ 0, we apply division lemma to 63 and 141, to get
141 = 63 x 2 + 15
Step 3: We consider the new divisor 63 and the new remainder 15, and apply the division lemma to get
63 = 15 x 4 + 3
We consider the new divisor 15 and the new remainder 3, and apply the division lemma to get
15 = 3 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 141 and 204 is 3
Notice that 3 = HCF(15,3) = HCF(63,15) = HCF(141,63) = HCF(204,141) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 330 > 3, we apply the division lemma to 330 and 3, to get
330 = 3 x 110 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 330 is 3
Notice that 3 = HCF(330,3) .
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Frequently Asked Questions on HCF of 141, 204, 330 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 141, 204, 330?
Answer: HCF of 141, 204, 330 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 141, 204, 330 using Euclid's Algorithm?
Answer: For arbitrary numbers 141, 204, 330 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.