Highest Common Factor of 542, 912, 314 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 542, 912, 314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 912, 314 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 542, 912, 314 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 542, 912, 314 is 2.
HCF(542, 912, 314) = 2
HCF of 542, 912, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 542, 912, 314 is 2.
Highest Common Factor of 542,912,314 is 2
Step 1: Since 912 > 542, we apply the division lemma to 912 and 542, to get
912 = 542 x 1 + 370
Step 2: Since the reminder 542 ≠ 0, we apply division lemma to 370 and 542, to get
542 = 370 x 1 + 172
Step 3: We consider the new divisor 370 and the new remainder 172, and apply the division lemma to get
370 = 172 x 2 + 26
We consider the new divisor 172 and the new remainder 26,and apply the division lemma to get
172 = 26 x 6 + 16
We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get
26 = 16 x 1 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 542 and 912 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(172,26) = HCF(370,172) = HCF(542,370) = HCF(912,542) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 2, we apply the division lemma to 314 and 2, to get
314 = 2 x 157 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 314 is 2
Notice that 2 = HCF(314,2) .
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Frequently Asked Questions on HCF of 542, 912, 314 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 542, 912, 314?
Answer: HCF of 542, 912, 314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 912, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 912, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.