Highest Common Factor of 474, 780, 282 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 474, 780, 282 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 780, 282 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 474, 780, 282 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 474, 780, 282 is 6.
HCF(474, 780, 282) = 6
HCF of 474, 780, 282 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 474, 780, 282 is 6.
Highest Common Factor of 474,780,282 is 6
Step 1: Since 780 > 474, we apply the division lemma to 780 and 474, to get
780 = 474 x 1 + 306
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 306 and 474, to get
474 = 306 x 1 + 168
Step 3: We consider the new divisor 306 and the new remainder 168, and apply the division lemma to get
306 = 168 x 1 + 138
We consider the new divisor 168 and the new remainder 138,and apply the division lemma to get
168 = 138 x 1 + 30
We consider the new divisor 138 and the new remainder 30,and apply the division lemma to get
138 = 30 x 4 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
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 474 and 780 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(138,30) = HCF(168,138) = HCF(306,168) = HCF(474,306) = HCF(780,474) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 282 > 6, we apply the division lemma to 282 and 6, to get
282 = 6 x 47 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 282 is 6
Notice that 6 = HCF(282,6) .
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Frequently Asked Questions on HCF of 474, 780, 282 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 474, 780, 282?
Answer: HCF of 474, 780, 282 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 780, 282 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 780, 282 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.