Highest Common Factor of 174, 980, 548 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 174, 980, 548 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 980, 548 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 174, 980, 548 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 174, 980, 548 is 2.
HCF(174, 980, 548) = 2
HCF of 174, 980, 548 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 174, 980, 548 is 2.
Highest Common Factor of 174,980,548 is 2
Step 1: Since 980 > 174, we apply the division lemma to 980 and 174, to get
980 = 174 x 5 + 110
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 110 and 174, to get
174 = 110 x 1 + 64
Step 3: We consider the new divisor 110 and the new remainder 64, and apply the division lemma to get
110 = 64 x 1 + 46
We consider the new divisor 64 and the new remainder 46,and apply the division lemma to get
64 = 46 x 1 + 18
We consider the new divisor 46 and the new remainder 18,and apply the division lemma to get
46 = 18 x 2 + 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 174 and 980 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(46,18) = HCF(64,46) = HCF(110,64) = HCF(174,110) = HCF(980,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 548 > 2, we apply the division lemma to 548 and 2, to get
548 = 2 x 274 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 548 is 2
Notice that 2 = HCF(548,2) .
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Frequently Asked Questions on HCF of 174, 980, 548 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 174, 980, 548?
Answer: HCF of 174, 980, 548 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 980, 548 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 980, 548 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.