Highest Common Factor of 480, 1770, 2172 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, 1770, 2172 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 480, 1770, 2172 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, 1770, 2172 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, 1770, 2172 is 6.
HCF(480, 1770, 2172) = 6
HCF of 480, 1770, 2172 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, 1770, 2172 is 6.
Highest Common Factor of 480,1770,2172 is 6
Step 1: Since 1770 > 480, we apply the division lemma to 1770 and 480, to get
1770 = 480 x 3 + 330
Step 2: Since the reminder 480 ≠ 0, we apply division lemma to 330 and 480, to get
480 = 330 x 1 + 150
Step 3: We consider the new divisor 330 and the new remainder 150, and apply the division lemma to get
330 = 150 x 2 + 30
We consider the new divisor 150 and the new remainder 30, and apply the division lemma to get
150 = 30 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 480 and 1770 is 30
Notice that 30 = HCF(150,30) = HCF(330,150) = HCF(480,330) = HCF(1770,480) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2172 > 30, we apply the division lemma to 2172 and 30, to get
2172 = 30 x 72 + 12
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 12 and 30, to get
30 = 12 x 2 + 6
Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 2172 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(2172,30) .
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Frequently Asked Questions on HCF of 480, 1770, 2172 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, 1770, 2172?
Answer: HCF of 480, 1770, 2172 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 480, 1770, 2172 using Euclid's Algorithm?
Answer: For arbitrary numbers 480, 1770, 2172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.