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, 378 i.e. 54 the largest integer that leaves a remainder zero for all numbers.
HCF of 270, 378 is 54 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, 378 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, 378 is 54.
HCF(270, 378) = 54
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 270, 378 is 54.
Step 1: Since 378 > 270, we apply the division lemma to 378 and 270, to get
378 = 270 x 1 + 108
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 108 and 270, to get
270 = 108 x 2 + 54
Step 3: We consider the new divisor 108 and the new remainder 54, and apply the division lemma to get
108 = 54 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 270 and 378 is 54
Notice that 54 = HCF(108,54) = HCF(270,108) = HCF(378,270) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 378?
Answer: HCF of 270, 378 is 54 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 270, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 270, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.