Highest Common Factor of 104, 274 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 104, 274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 104, 274 is 2 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 104, 274 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 104, 274 is 2.
HCF(104, 274) = 2
HCF of 104, 274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 104, 274 is 2.
Highest Common Factor of 104,274 is 2
Step 1: Since 274 > 104, we apply the division lemma to 274 and 104, to get
274 = 104 x 2 + 66
Step 2: Since the reminder 104 ≠ 0, we apply division lemma to 66 and 104, to get
104 = 66 x 1 + 38
Step 3: We consider the new divisor 66 and the new remainder 38, and apply the division lemma to get
66 = 38 x 1 + 28
We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get
38 = 28 x 1 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 104 and 274 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(104,66) = HCF(274,104) .
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Frequently Asked Questions on HCF of 104, 274 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 104, 274?
Answer: HCF of 104, 274 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 104, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 104, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.