Highest Common Factor of 678, 394, 44 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 678, 394, 44 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 394, 44 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 678, 394, 44 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 678, 394, 44 is 2.
HCF(678, 394, 44) = 2
HCF of 678, 394, 44 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 394, 44 is 2.
Highest Common Factor of 678,394,44 is 2
Step 1: Since 678 > 394, we apply the division lemma to 678 and 394, to get
678 = 394 x 1 + 284
Step 2: Since the reminder 394 ≠ 0, we apply division lemma to 284 and 394, to get
394 = 284 x 1 + 110
Step 3: We consider the new divisor 284 and the new remainder 110, and apply the division lemma to get
284 = 110 x 2 + 64
We consider the new divisor 110 and the new remainder 64,and apply the division lemma to get
110 = 64 x 1 + 46
We consider the new divisor 64 and the new remainder 46,and apply the division lemma to get
64 = 46 x 1 + 18
We consider the new divisor 46 and the new remainder 18,and apply the division lemma to get
46 = 18 x 2 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 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 678 and 394 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(64,46) = HCF(110,64) = HCF(284,110) = HCF(394,284) = HCF(678,394) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 44 > 2, we apply the division lemma to 44 and 2, to get
44 = 2 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 44 is 2
Notice that 2 = HCF(44,2) .
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Frequently Asked Questions on HCF of 678, 394, 44 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 678, 394, 44?
Answer: HCF of 678, 394, 44 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 394, 44 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 394, 44 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.