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 312, 529, 249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 529, 249 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 312, 529, 249 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 312, 529, 249 is 1.
HCF(312, 529, 249) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 529, 249 is 1.
Step 1: Since 529 > 312, we apply the division lemma to 529 and 312, to get
529 = 312 x 1 + 217
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 217 and 312, to get
312 = 217 x 1 + 95
Step 3: We consider the new divisor 217 and the new remainder 95, and apply the division lemma to get
217 = 95 x 2 + 27
We consider the new divisor 95 and the new remainder 27,and apply the division lemma to get
95 = 27 x 3 + 14
We consider the new divisor 27 and the new remainder 14,and apply the division lemma to get
27 = 14 x 1 + 13
We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get
14 = 13 x 1 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 312 and 529 is 1
Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(27,14) = HCF(95,27) = HCF(217,95) = HCF(312,217) = HCF(529,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 249 > 1, we apply the division lemma to 249 and 1, to get
249 = 1 x 249 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 249 is 1
Notice that 1 = HCF(249,1) .
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 312, 529, 249?
Answer: HCF of 312, 529, 249 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 529, 249 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 529, 249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.