Highest Common Factor of 474, 783, 84 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, 783, 84 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 783, 84 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 474, 783, 84 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, 783, 84 is 3.
HCF(474, 783, 84) = 3
HCF of 474, 783, 84 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, 783, 84 is 3.
Highest Common Factor of 474,783,84 is 3
Step 1: Since 783 > 474, we apply the division lemma to 783 and 474, to get
783 = 474 x 1 + 309
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 309 and 474, to get
474 = 309 x 1 + 165
Step 3: We consider the new divisor 309 and the new remainder 165, and apply the division lemma to get
309 = 165 x 1 + 144
We consider the new divisor 165 and the new remainder 144,and apply the division lemma to get
165 = 144 x 1 + 21
We consider the new divisor 144 and the new remainder 21,and apply the division lemma to get
144 = 21 x 6 + 18
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 474 and 783 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(144,21) = HCF(165,144) = HCF(309,165) = HCF(474,309) = HCF(783,474) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 84 > 3, we apply the division lemma to 84 and 3, to get
84 = 3 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 84 is 3
Notice that 3 = HCF(84,3) .
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Frequently Asked Questions on HCF of 474, 783, 84 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, 783, 84?
Answer: HCF of 474, 783, 84 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 783, 84 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 783, 84 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.