Highest Common Factor of 754, 54174 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 754, 54174 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 54174 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 754, 54174 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 754, 54174 is 2.
HCF(754, 54174) = 2
HCF of 754, 54174 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 54174 is 2.
Highest Common Factor of 754,54174 is 2
Step 1: Since 54174 > 754, we apply the division lemma to 54174 and 754, to get
54174 = 754 x 71 + 640
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 640 and 754, to get
754 = 640 x 1 + 114
Step 3: We consider the new divisor 640 and the new remainder 114, and apply the division lemma to get
640 = 114 x 5 + 70
We consider the new divisor 114 and the new remainder 70,and apply the division lemma to get
114 = 70 x 1 + 44
We consider the new divisor 70 and the new remainder 44,and apply the division lemma to get
70 = 44 x 1 + 26
We consider the new divisor 44 and the new remainder 26,and apply the division lemma to get
44 = 26 x 1 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 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 754 and 54174 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(44,26) = HCF(70,44) = HCF(114,70) = HCF(640,114) = HCF(754,640) = HCF(54174,754) .
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Frequently Asked Questions on HCF of 754, 54174 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 754, 54174?
Answer: HCF of 754, 54174 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 54174 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 54174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
