Highest Common Factor of 780, 300, 141 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 780, 300, 141 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 780, 300, 141 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 780, 300, 141 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 780, 300, 141 is 3.
HCF(780, 300, 141) = 3
HCF of 780, 300, 141 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 780, 300, 141 is 3.
Highest Common Factor of 780,300,141 is 3
Step 1: Since 780 > 300, we apply the division lemma to 780 and 300, to get
780 = 300 x 2 + 180
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 180 and 300, to get
300 = 180 x 1 + 120
Step 3: We consider the new divisor 180 and the new remainder 120, and apply the division lemma to get
180 = 120 x 1 + 60
We consider the new divisor 120 and the new remainder 60, and apply the division lemma to get
120 = 60 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 60, the HCF of 780 and 300 is 60
Notice that 60 = HCF(120,60) = HCF(180,120) = HCF(300,180) = HCF(780,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 141 > 60, we apply the division lemma to 141 and 60, to get
141 = 60 x 2 + 21
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 21 and 60, to get
60 = 21 x 2 + 18
Step 3: We consider the new divisor 21 and the new remainder 18, and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3, and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 60 and 141 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(60,21) = HCF(141,60) .
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Frequently Asked Questions on HCF of 780, 300, 141 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 780, 300, 141?
Answer: HCF of 780, 300, 141 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 780, 300, 141 using Euclid's Algorithm?
Answer: For arbitrary numbers 780, 300, 141 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.