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 272, 397, 110, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 272, 397, 110, 14 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 272, 397, 110, 14 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 272, 397, 110, 14 is 1.
HCF(272, 397, 110, 14) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 272, 397, 110, 14 is 1.
Step 1: Since 397 > 272, we apply the division lemma to 397 and 272, to get
397 = 272 x 1 + 125
Step 2: Since the reminder 272 ≠ 0, we apply division lemma to 125 and 272, to get
272 = 125 x 2 + 22
Step 3: We consider the new divisor 125 and the new remainder 22, and apply the division lemma to get
125 = 22 x 5 + 15
We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get
22 = 15 x 1 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 272 and 397 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(125,22) = HCF(272,125) = HCF(397,272) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 110 > 1, we apply the division lemma to 110 and 1, to get
110 = 1 x 110 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 110 is 1
Notice that 1 = HCF(110,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 14 > 1, we apply the division lemma to 14 and 1, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 14 is 1
Notice that 1 = HCF(14,1) .
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 272, 397, 110, 14?
Answer: HCF of 272, 397, 110, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 272, 397, 110, 14 using Euclid's Algorithm?
Answer: For arbitrary numbers 272, 397, 110, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.