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 378, 216 i.e. 54 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 216 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 378, 216 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 378, 216 is 54.
HCF(378, 216) = 54
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 216 is 54.
Step 1: Since 378 > 216, we apply the division lemma to 378 and 216, to get
378 = 216 x 1 + 162
Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 162 and 216, to get
216 = 162 x 1 + 54
Step 3: We consider the new divisor 162 and the new remainder 54, and apply the division lemma to get
162 = 54 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 54, the HCF of 378 and 216 is 54
Notice that 54 = HCF(162,54) = HCF(216,162) = HCF(378,216) .
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 378, 216?
Answer: HCF of 378, 216 is 54 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 216 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.