Highest Common Factor of 720, 993, 297 using Euclid's algorithm
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, 993, 297 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 993, 297 is 3 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, 993, 297 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, 993, 297 is 3.
HCF(720, 993, 297) = 3
HCF of 720, 993, 297 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 993, 297 is 3.
Highest Common Factor of 720,993,297 is 3
Step 1: Since 993 > 720, we apply the division lemma to 993 and 720, to get
993 = 720 x 1 + 273
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 273 and 720, to get
720 = 273 x 2 + 174
Step 3: We consider the new divisor 273 and the new remainder 174, and apply the division lemma to get
273 = 174 x 1 + 99
We consider the new divisor 174 and the new remainder 99,and apply the division lemma to get
174 = 99 x 1 + 75
We consider the new divisor 99 and the new remainder 75,and apply the division lemma to get
99 = 75 x 1 + 24
We consider the new divisor 75 and the new remainder 24,and apply the division lemma to get
75 = 24 x 3 + 3
We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get
24 = 3 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 720 and 993 is 3
Notice that 3 = HCF(24,3) = HCF(75,24) = HCF(99,75) = HCF(174,99) = HCF(273,174) = HCF(720,273) = HCF(993,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 297 > 3, we apply the division lemma to 297 and 3, to get
297 = 3 x 99 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 297 is 3
Notice that 3 = HCF(297,3) .
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Frequently Asked Questions on HCF of 720, 993, 297 using Euclid's Algorithm
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, 993, 297?
Answer: HCF of 720, 993, 297 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 993, 297 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 993, 297 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.