Highest Common Factor of 548, 318 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 548, 318 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 548, 318 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 548, 318 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 548, 318 is 2.
HCF(548, 318) = 2
HCF of 548, 318 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 548, 318 is 2.
Highest Common Factor of 548,318 is 2
Step 1: Since 548 > 318, we apply the division lemma to 548 and 318, to get
548 = 318 x 1 + 230
Step 2: Since the reminder 318 ≠ 0, we apply division lemma to 230 and 318, to get
318 = 230 x 1 + 88
Step 3: We consider the new divisor 230 and the new remainder 88, and apply the division lemma to get
230 = 88 x 2 + 54
We consider the new divisor 88 and the new remainder 54,and apply the division lemma to get
88 = 54 x 1 + 34
We consider the new divisor 54 and the new remainder 34,and apply the division lemma to get
54 = 34 x 1 + 20
We consider the new divisor 34 and the new remainder 20,and apply the division lemma to get
34 = 20 x 1 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 548 and 318 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(34,20) = HCF(54,34) = HCF(88,54) = HCF(230,88) = HCF(318,230) = HCF(548,318) .
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Frequently Asked Questions on HCF of 548, 318 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 548, 318?
Answer: HCF of 548, 318 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 548, 318 using Euclid's Algorithm?
Answer: For arbitrary numbers 548, 318 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.