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 720, 244, 115 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 244, 115 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 720, 244, 115 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 720, 244, 115 is 1.
HCF(720, 244, 115) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 244, 115 is 1.
Step 1: Since 720 > 244, we apply the division lemma to 720 and 244, to get
720 = 244 x 2 + 232
Step 2: Since the reminder 244 ≠ 0, we apply division lemma to 232 and 244, to get
244 = 232 x 1 + 12
Step 3: We consider the new divisor 232 and the new remainder 12, and apply the division lemma to get
232 = 12 x 19 + 4
We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 720 and 244 is 4
Notice that 4 = HCF(12,4) = HCF(232,12) = HCF(244,232) = HCF(720,244) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 115 > 4, we apply the division lemma to 115 and 4, to get
115 = 4 x 28 + 3
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get
4 = 3 x 1 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 115 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(115,4) .
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 720, 244, 115?
Answer: HCF of 720, 244, 115 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 244, 115 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 244, 115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.