Highest Common Factor of 288, 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 288, 174 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 288, 174 is 6 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 288, 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 288, 174 is 6.
HCF(288, 174) = 6
HCF of 288, 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 288, 174 is 6.
Highest Common Factor of 288,174 is 6
Step 1: Since 288 > 174, we apply the division lemma to 288 and 174, to get
288 = 174 x 1 + 114
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 114 and 174, to get
174 = 114 x 1 + 60
Step 3: We consider the new divisor 114 and the new remainder 60, and apply the division lemma to get
114 = 60 x 1 + 54
We consider the new divisor 60 and the new remainder 54,and apply the division lemma to get
60 = 54 x 1 + 6
We consider the new divisor 54 and the new remainder 6,and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 288 and 174 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(114,60) = HCF(174,114) = HCF(288,174) .
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Frequently Asked Questions on HCF of 288, 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 288, 174?
Answer: HCF of 288, 174 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 288, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 288, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.