Highest Common Factor of 548, 496, 174 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, 496, 174 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 548, 496, 174 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, 496, 174 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, 496, 174 is 2.
HCF(548, 496, 174) = 2
HCF of 548, 496, 174 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, 496, 174 is 2.
Highest Common Factor of 548,496,174 is 2
Step 1: Since 548 > 496, we apply the division lemma to 548 and 496, to get
548 = 496 x 1 + 52
Step 2: Since the reminder 496 ≠ 0, we apply division lemma to 52 and 496, to get
496 = 52 x 9 + 28
Step 3: We consider the new divisor 52 and the new remainder 28, and apply the division lemma to get
52 = 28 x 1 + 24
We consider the new divisor 28 and the new remainder 24,and apply the division lemma to get
28 = 24 x 1 + 4
We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 548 and 496 is 4
Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(52,28) = HCF(496,52) = HCF(548,496) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 4, we apply the division lemma to 174 and 4, to get
174 = 4 x 43 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 174 is 2
Notice that 2 = HCF(4,2) = HCF(174,4) .
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Frequently Asked Questions on HCF of 548, 496, 174 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, 496, 174?
Answer: HCF of 548, 496, 174 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 548, 496, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 548, 496, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.