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, 80, 294, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 297, 80, 294, 407 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, 80, 294, 407 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, 80, 294, 407 is 1.
HCF(297, 80, 294, 407) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 297, 80, 294, 407 is 1.
Step 1: Since 297 > 80, we apply the division lemma to 297 and 80, to get
297 = 80 x 3 + 57
Step 2: Since the reminder 80 ≠ 0, we apply division lemma to 57 and 80, to get
80 = 57 x 1 + 23
Step 3: We consider the new divisor 57 and the new remainder 23, and apply the division lemma to get
57 = 23 x 2 + 11
We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get
23 = 11 x 2 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 297 and 80 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(57,23) = HCF(80,57) = HCF(297,80) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 294 > 1, we apply the division lemma to 294 and 1, to get
294 = 1 x 294 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 294 is 1
Notice that 1 = HCF(294,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 1, we apply the division lemma to 407 and 1, to get
407 = 1 x 407 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 407 is 1
Notice that 1 = HCF(407,1) .
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 297, 80, 294, 407?
Answer: HCF of 297, 80, 294, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 297, 80, 294, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 297, 80, 294, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.