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 317, 564, 287, 800 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 317, 564, 287, 800 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 317, 564, 287, 800 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 317, 564, 287, 800 is 1.
HCF(317, 564, 287, 800) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 317, 564, 287, 800 is 1.
Step 1: Since 564 > 317, we apply the division lemma to 564 and 317, to get
564 = 317 x 1 + 247
Step 2: Since the reminder 317 ≠ 0, we apply division lemma to 247 and 317, to get
317 = 247 x 1 + 70
Step 3: We consider the new divisor 247 and the new remainder 70, and apply the division lemma to get
247 = 70 x 3 + 37
We consider the new divisor 70 and the new remainder 37,and apply the division lemma to get
70 = 37 x 1 + 33
We consider the new divisor 37 and the new remainder 33,and apply the division lemma to get
37 = 33 x 1 + 4
We consider the new divisor 33 and the new remainder 4,and apply the division lemma to get
33 = 4 x 8 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 317 and 564 is 1
Notice that 1 = HCF(4,1) = HCF(33,4) = HCF(37,33) = HCF(70,37) = HCF(247,70) = HCF(317,247) = HCF(564,317) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 287 > 1, we apply the division lemma to 287 and 1, to get
287 = 1 x 287 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 287 is 1
Notice that 1 = HCF(287,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 800 > 1, we apply the division lemma to 800 and 1, to get
800 = 1 x 800 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 800 is 1
Notice that 1 = HCF(800,1) .
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 317, 564, 287, 800?
Answer: HCF of 317, 564, 287, 800 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 317, 564, 287, 800 using Euclid's Algorithm?
Answer: For arbitrary numbers 317, 564, 287, 800 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.