Highest Common Factor of 480, 270, 114 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 480, 270, 114 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 480, 270, 114 is 6 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 480, 270, 114 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 480, 270, 114 is 6.
HCF(480, 270, 114) = 6
HCF of 480, 270, 114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 480, 270, 114 is 6.
Highest Common Factor of 480,270,114 is 6
Step 1: Since 480 > 270, we apply the division lemma to 480 and 270, to get
480 = 270 x 1 + 210
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 210 and 270, to get
270 = 210 x 1 + 60
Step 3: We consider the new divisor 210 and the new remainder 60, and apply the division lemma to get
210 = 60 x 3 + 30
We consider the new divisor 60 and the new remainder 30, and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 480 and 270 is 30
Notice that 30 = HCF(60,30) = HCF(210,60) = HCF(270,210) = HCF(480,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 30, we apply the division lemma to 114 and 30, to get
114 = 30 x 3 + 24
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 24 and 30, to get
30 = 24 x 1 + 6
Step 3: We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 114 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(114,30) .
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Frequently Asked Questions on HCF of 480, 270, 114 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 480, 270, 114?
Answer: HCF of 480, 270, 114 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 480, 270, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 480, 270, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.