Highest Common Factor of 81, 54, 74 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 81, 54, 74 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 81, 54, 74 is 1 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 81, 54, 74 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 81, 54, 74 is 1.
HCF(81, 54, 74) = 1
HCF of 81, 54, 74 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 81, 54, 74 is 1.
Highest Common Factor of 81,54,74 is 1
Step 1: Since 81 > 54, we apply the division lemma to 81 and 54, to get
81 = 54 x 1 + 27
Step 2: Since the reminder 54 ≠ 0, we apply division lemma to 27 and 54, to get
54 = 27 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 81 and 54 is 27
Notice that 27 = HCF(54,27) = HCF(81,54) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 27, we apply the division lemma to 74 and 27, to get
74 = 27 x 2 + 20
Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 20 and 27, to get
27 = 20 x 1 + 7
Step 3: We consider the new divisor 20 and the new remainder 7, and apply the division lemma to get
20 = 7 x 2 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 27 and 74 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(74,27) .
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Frequently Asked Questions on HCF of 81, 54, 74 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 81, 54, 74?
Answer: HCF of 81, 54, 74 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 81, 54, 74 using Euclid's Algorithm?
Answer: For arbitrary numbers 81, 54, 74 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.