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 293, 1128, 1720 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 293, 1128, 1720 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 293, 1128, 1720 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 293, 1128, 1720 is 1.
HCF(293, 1128, 1720) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 293, 1128, 1720 is 1.
Step 1: Since 1128 > 293, we apply the division lemma to 1128 and 293, to get
1128 = 293 x 3 + 249
Step 2: Since the reminder 293 ≠ 0, we apply division lemma to 249 and 293, to get
293 = 249 x 1 + 44
Step 3: We consider the new divisor 249 and the new remainder 44, and apply the division lemma to get
249 = 44 x 5 + 29
We consider the new divisor 44 and the new remainder 29,and apply the division lemma to get
44 = 29 x 1 + 15
We consider the new divisor 29 and the new remainder 15,and apply the division lemma to get
29 = 15 x 1 + 14
We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get
15 = 14 x 1 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma 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 293 and 1128 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(29,15) = HCF(44,29) = HCF(249,44) = HCF(293,249) = HCF(1128,293) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1720 > 1, we apply the division lemma to 1720 and 1, to get
1720 = 1 x 1720 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1720 is 1
Notice that 1 = HCF(1720,1) .
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 293, 1128, 1720?
Answer: HCF of 293, 1128, 1720 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 293, 1128, 1720 using Euclid's Algorithm?
Answer: For arbitrary numbers 293, 1128, 1720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.