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 500, 683, 237 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 683, 237 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 500, 683, 237 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 500, 683, 237 is 1.
HCF(500, 683, 237) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 683, 237 is 1.
Step 1: Since 683 > 500, we apply the division lemma to 683 and 500, to get
683 = 500 x 1 + 183
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 183 and 500, to get
500 = 183 x 2 + 134
Step 3: We consider the new divisor 183 and the new remainder 134, and apply the division lemma to get
183 = 134 x 1 + 49
We consider the new divisor 134 and the new remainder 49,and apply the division lemma to get
134 = 49 x 2 + 36
We consider the new divisor 49 and the new remainder 36,and apply the division lemma to get
49 = 36 x 1 + 13
We consider the new divisor 36 and the new remainder 13,and apply the division lemma to get
36 = 13 x 2 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 500 and 683 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(36,13) = HCF(49,36) = HCF(134,49) = HCF(183,134) = HCF(500,183) = HCF(683,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 237 > 1, we apply the division lemma to 237 and 1, to get
237 = 1 x 237 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 237 is 1
Notice that 1 = HCF(237,1) .
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 500, 683, 237?
Answer: HCF of 500, 683, 237 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 683, 237 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 683, 237 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.