Highest Common Factor of 474, 293, 104 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, 293, 104 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 474, 293, 104 is 1 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, 293, 104 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, 293, 104 is 1.
HCF(474, 293, 104) = 1
HCF of 474, 293, 104 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, 293, 104 is 1.
Highest Common Factor of 474,293,104 is 1
Step 1: Since 474 > 293, we apply the division lemma to 474 and 293, to get
474 = 293 x 1 + 181
Step 2: Since the reminder 293 ≠ 0, we apply division lemma to 181 and 293, to get
293 = 181 x 1 + 112
Step 3: We consider the new divisor 181 and the new remainder 112, and apply the division lemma to get
181 = 112 x 1 + 69
We consider the new divisor 112 and the new remainder 69,and apply the division lemma to get
112 = 69 x 1 + 43
We consider the new divisor 69 and the new remainder 43,and apply the division lemma to get
69 = 43 x 1 + 26
We consider the new divisor 43 and the new remainder 26,and apply the division lemma to get
43 = 26 x 1 + 17
We consider the new divisor 26 and the new remainder 17,and apply the division lemma to get
26 = 17 x 1 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 474 and 293 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(26,17) = HCF(43,26) = HCF(69,43) = HCF(112,69) = HCF(181,112) = HCF(293,181) = HCF(474,293) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 104 > 1, we apply the division lemma to 104 and 1, to get
104 = 1 x 104 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 104 is 1
Notice that 1 = HCF(104,1) .
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Frequently Asked Questions on HCF of 474, 293, 104 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, 293, 104?
Answer: HCF of 474, 293, 104 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 474, 293, 104 using Euclid's Algorithm?
Answer: For arbitrary numbers 474, 293, 104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
