Highest Common Factor of 75, 30, 114 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 75, 30, 114 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 75, 30, 114 is 3 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 75, 30, 114 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 75, 30, 114 is 3.
HCF(75, 30, 114) = 3
HCF of 75, 30, 114 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 75, 30, 114 is 3.
Highest Common Factor of 75,30,114 is 3
Step 1: Since 75 > 30, we apply the division lemma to 75 and 30, to get
75 = 30 x 2 + 15
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 15 and 30, to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 75 and 30 is 15
Notice that 15 = HCF(30,15) = HCF(75,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 15, we apply the division lemma to 114 and 15, to get
114 = 15 x 7 + 9
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 9 and 15, to get
15 = 9 x 1 + 6
Step 3: We consider the new divisor 9 and the new remainder 6, and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 114 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(114,15) .
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Frequently Asked Questions on HCF of 75, 30, 114 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 75, 30, 114?
Answer: HCF of 75, 30, 114 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 75, 30, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 75, 30, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.