Highest Common Factor of 30, 60, 54, 65 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 30, 60, 54, 65 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 30, 60, 54, 65 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 30, 60, 54, 65 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 30, 60, 54, 65 is 1.
HCF(30, 60, 54, 65) = 1
HCF of 30, 60, 54, 65 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 30, 60, 54, 65 is 1.
Highest Common Factor of 30,60,54,65 is 1
Step 1: Since 60 > 30, we apply the division lemma to 60 and 30, to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 30 and 60 is 30
Notice that 30 = HCF(60,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 30, we apply the division lemma to 54 and 30, to get
54 = 30 x 1 + 24
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 24 and 30, to get
30 = 24 x 1 + 6
Step 3: We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 54 is 6
Notice that 6 = HCF(24,6) = HCF(30,24) = HCF(54,30) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 65 > 6, we apply the division lemma to 65 and 6, to get
65 = 6 x 10 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 65 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(65,6) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 30, 60, 54, 65 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 30, 60, 54, 65?
Answer: HCF of 30, 60, 54, 65 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 30, 60, 54, 65 using Euclid's Algorithm?
Answer: For arbitrary numbers 30, 60, 54, 65 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.