Highest Common Factor of 75, 90, 87, 108 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, 90, 87, 108 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 75, 90, 87, 108 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, 90, 87, 108 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, 90, 87, 108 is 3.
HCF(75, 90, 87, 108) = 3
HCF of 75, 90, 87, 108 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, 90, 87, 108 is 3.
Highest Common Factor of 75,90,87,108 is 3
Step 1: Since 90 > 75, we apply the division lemma to 90 and 75, to get
90 = 75 x 1 + 15
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 15 and 75, to get
75 = 15 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 75 and 90 is 15
Notice that 15 = HCF(75,15) = HCF(90,75) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 87 > 15, we apply the division lemma to 87 and 15, to get
87 = 15 x 5 + 12
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 12 and 15, to get
15 = 12 x 1 + 3
Step 3: We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 87 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(87,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 3, we apply the division lemma to 108 and 3, to get
108 = 3 x 36 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 108 is 3
Notice that 3 = HCF(108,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 75, 90, 87, 108 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, 90, 87, 108?
Answer: HCF of 75, 90, 87, 108 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 75, 90, 87, 108 using Euclid's Algorithm?
Answer: For arbitrary numbers 75, 90, 87, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.