Highest Common Factor of 314, 535, 103 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, 535, 103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 535, 103 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 314, 535, 103 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, 535, 103 is 1.
HCF(314, 535, 103) = 1
HCF of 314, 535, 103 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, 535, 103 is 1.
Highest Common Factor of 314,535,103 is 1
Step 1: Since 535 > 314, we apply the division lemma to 535 and 314, to get
535 = 314 x 1 + 221
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 221 and 314, to get
314 = 221 x 1 + 93
Step 3: We consider the new divisor 221 and the new remainder 93, and apply the division lemma to get
221 = 93 x 2 + 35
We consider the new divisor 93 and the new remainder 35,and apply the division lemma to get
93 = 35 x 2 + 23
We consider the new divisor 35 and the new remainder 23,and apply the division lemma to get
35 = 23 x 1 + 12
We consider the new divisor 23 and the new remainder 12,and apply the division lemma to get
23 = 12 x 1 + 11
We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get
12 = 11 x 1 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 314 and 535 is 1
Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(23,12) = HCF(35,23) = HCF(93,35) = HCF(221,93) = HCF(314,221) = HCF(535,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get
103 = 1 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1
Notice that 1 = HCF(103,1) .
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Frequently Asked Questions on HCF of 314, 535, 103 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, 535, 103?
Answer: HCF of 314, 535, 103 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 535, 103 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 535, 103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.