Highest Common Factor of 270, 60, 348 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 270, 60, 348 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 60, 348 is 6 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 270, 60, 348 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 270, 60, 348 is 6.
HCF(270, 60, 348) = 6
HCF of 270, 60, 348 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 60, 348 is 6.
Highest Common Factor of 270,60,348 is 6
Step 1: Since 270 > 60, we apply the division lemma to 270 and 60, to get
270 = 60 x 4 + 30
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 30 and 60, 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 270 and 60 is 30
Notice that 30 = HCF(60,30) = HCF(270,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 348 > 30, we apply the division lemma to 348 and 30, to get
348 = 30 x 11 + 18
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 18 and 30, to get
30 = 18 x 1 + 12
Step 3: We consider the new divisor 18 and the new remainder 12, and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 348 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(348,30) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 270, 60, 348 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 270, 60, 348?
Answer: HCF of 270, 60, 348 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 60, 348 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 60, 348 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.