Highest Common Factor of 314, 748, 278 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 314, 748, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 748, 278 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 314, 748, 278 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 314, 748, 278 is 2.
HCF(314, 748, 278) = 2
HCF of 314, 748, 278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 314, 748, 278 is 2.
Highest Common Factor of 314,748,278 is 2
Step 1: Since 748 > 314, we apply the division lemma to 748 and 314, to get
748 = 314 x 2 + 120
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 120 and 314, to get
314 = 120 x 2 + 74
Step 3: We consider the new divisor 120 and the new remainder 74, and apply the division lemma to get
120 = 74 x 1 + 46
We consider the new divisor 74 and the new remainder 46,and apply the division lemma to get
74 = 46 x 1 + 28
We consider the new divisor 46 and the new remainder 28,and apply the division lemma to get
46 = 28 x 1 + 18
We consider the new divisor 28 and the new remainder 18,and apply the division lemma to get
28 = 18 x 1 + 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 314 and 748 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(46,28) = HCF(74,46) = HCF(120,74) = HCF(314,120) = HCF(748,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 2, we apply the division lemma to 278 and 2, to get
278 = 2 x 139 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 278 is 2
Notice that 2 = HCF(278,2) .
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Frequently Asked Questions on HCF of 314, 748, 278 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 314, 748, 278?
Answer: HCF of 314, 748, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 748, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 748, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.