Highest Common Factor of 548, 678 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, 678 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 548, 678 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, 678 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, 678 is 2.
HCF(548, 678) = 2
HCF of 548, 678 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, 678 is 2.
Highest Common Factor of 548,678 is 2
Step 1: Since 678 > 548, we apply the division lemma to 678 and 548, to get
678 = 548 x 1 + 130
Step 2: Since the reminder 548 ≠ 0, we apply division lemma to 130 and 548, to get
548 = 130 x 4 + 28
Step 3: We consider the new divisor 130 and the new remainder 28, and apply the division lemma to get
130 = 28 x 4 + 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 548 and 678 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(130,28) = HCF(548,130) = HCF(678,548) .
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Frequently Asked Questions on HCF of 548, 678 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, 678?
Answer: HCF of 548, 678 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 548, 678 using Euclid's Algorithm?
Answer: For arbitrary numbers 548, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.