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 144, 216, 254 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 144, 216, 254 is 2 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 144, 216, 254 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 144, 216, 254 is 2.
HCF(144, 216, 254) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 144, 216, 254 is 2.
Step 1: Since 216 > 144, we apply the division lemma to 216 and 144, to get
216 = 144 x 1 + 72
Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 72 and 144, to get
144 = 72 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 72, the HCF of 144 and 216 is 72
Notice that 72 = HCF(144,72) = HCF(216,144) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 254 > 72, we apply the division lemma to 254 and 72, to get
254 = 72 x 3 + 38
Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 38 and 72, to get
72 = 38 x 1 + 34
Step 3: We consider the new divisor 38 and the new remainder 34, and apply the division lemma to get
38 = 34 x 1 + 4
We consider the new divisor 34 and the new remainder 4,and apply the division lemma to get
34 = 4 x 8 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 72 and 254 is 2
Notice that 2 = HCF(4,2) = HCF(34,4) = HCF(38,34) = HCF(72,38) = HCF(254,72) .
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 144, 216, 254?
Answer: HCF of 144, 216, 254 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 144, 216, 254 using Euclid's Algorithm?
Answer: For arbitrary numbers 144, 216, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.