Highest Common Factor of 312, 831, 735 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, 831, 735 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 831, 735 is 3 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, 831, 735 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, 831, 735 is 3.
HCF(312, 831, 735) = 3
HCF of 312, 831, 735 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, 831, 735 is 3.
Highest Common Factor of 312,831,735 is 3
Step 1: Since 831 > 312, we apply the division lemma to 831 and 312, to get
831 = 312 x 2 + 207
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 207 and 312, to get
312 = 207 x 1 + 105
Step 3: We consider the new divisor 207 and the new remainder 105, and apply the division lemma to get
207 = 105 x 1 + 102
We consider the new divisor 105 and the new remainder 102,and apply the division lemma to get
105 = 102 x 1 + 3
We consider the new divisor 102 and the new remainder 3,and apply the division lemma to get
102 = 3 x 34 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 312 and 831 is 3
Notice that 3 = HCF(102,3) = HCF(105,102) = HCF(207,105) = HCF(312,207) = HCF(831,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 3, we apply the division lemma to 735 and 3, to get
735 = 3 x 245 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 735 is 3
Notice that 3 = HCF(735,3) .
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, 831, 735 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, 831, 735?
Answer: HCF of 312, 831, 735 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 831, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 831, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.