Highest Common Factor of 282, 720, 447 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 282, 720, 447 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 282, 720, 447 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 282, 720, 447 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 282, 720, 447 is 3.
HCF(282, 720, 447) = 3
HCF of 282, 720, 447 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 282, 720, 447 is 3.
Highest Common Factor of 282,720,447 is 3
Step 1: Since 720 > 282, we apply the division lemma to 720 and 282, to get
720 = 282 x 2 + 156
Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 156 and 282, to get
282 = 156 x 1 + 126
Step 3: We consider the new divisor 156 and the new remainder 126, and apply the division lemma to get
156 = 126 x 1 + 30
We consider the new divisor 126 and the new remainder 30,and apply the division lemma to get
126 = 30 x 4 + 6
We consider the new divisor 30 and the new remainder 6,and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 282 and 720 is 6
Notice that 6 = HCF(30,6) = HCF(126,30) = HCF(156,126) = HCF(282,156) = HCF(720,282) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 447 > 6, we apply the division lemma to 447 and 6, to get
447 = 6 x 74 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 447 is 3
Notice that 3 = HCF(6,3) = HCF(447,6) .
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Frequently Asked Questions on HCF of 282, 720, 447 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 282, 720, 447?
Answer: HCF of 282, 720, 447 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 282, 720, 447 using Euclid's Algorithm?
Answer: For arbitrary numbers 282, 720, 447 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.