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 297, 715, 273 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 297, 715, 273 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 297, 715, 273 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 297, 715, 273 is 1.
HCF(297, 715, 273) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 297, 715, 273 is 1.
Step 1: Since 715 > 297, we apply the division lemma to 715 and 297, to get
715 = 297 x 2 + 121
Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 121 and 297, to get
297 = 121 x 2 + 55
Step 3: We consider the new divisor 121 and the new remainder 55, and apply the division lemma to get
121 = 55 x 2 + 11
We consider the new divisor 55 and the new remainder 11, and apply the division lemma to get
55 = 11 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 297 and 715 is 11
Notice that 11 = HCF(55,11) = HCF(121,55) = HCF(297,121) = HCF(715,297) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 273 > 11, we apply the division lemma to 273 and 11, to get
273 = 11 x 24 + 9
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 9 and 11, to get
11 = 9 x 1 + 2
Step 3: We consider the new divisor 9 and the new remainder 2, and apply the division lemma to get
9 = 2 x 4 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 11 and 273 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(273,11) .
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 297, 715, 273?
Answer: HCF of 297, 715, 273 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 297, 715, 273 using Euclid's Algorithm?
Answer: For arbitrary numbers 297, 715, 273 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.