Highest Common Factor of 312, 730, 186, 199 using Euclid's algorithm
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, 730, 186, 199 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 730, 186, 199 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, 730, 186, 199 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, 730, 186, 199 is 1.
HCF(312, 730, 186, 199) = 1
HCF of 312, 730, 186, 199 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 730, 186, 199 is 1.
Highest Common Factor of 312,730,186,199 is 1
Step 1: Since 730 > 312, we apply the division lemma to 730 and 312, to get
730 = 312 x 2 + 106
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 106 and 312, to get
312 = 106 x 2 + 100
Step 3: We consider the new divisor 106 and the new remainder 100, and apply the division lemma to get
106 = 100 x 1 + 6
We consider the new divisor 100 and the new remainder 6,and apply the division lemma to get
100 = 6 x 16 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 312 and 730 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(100,6) = HCF(106,100) = HCF(312,106) = HCF(730,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 186 > 2, we apply the division lemma to 186 and 2, to get
186 = 2 x 93 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 186 is 2
Notice that 2 = HCF(186,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 199 > 2, we apply the division lemma to 199 and 2, to get
199 = 2 x 99 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 199 is 1
Notice that 1 = HCF(2,1) = HCF(199,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 312, 730, 186, 199 using Euclid's Algorithm
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, 730, 186, 199?
Answer: HCF of 312, 730, 186, 199 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 730, 186, 199 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 730, 186, 199 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
