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, 845 i.e. 13 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 845 is 13 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, 845 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, 845 is 13.
HCF(312, 845) = 13
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 845 is 13.
Step 1: Since 845 > 312, we apply the division lemma to 845 and 312, to get
845 = 312 x 2 + 221
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 221 and 312, to get
312 = 221 x 1 + 91
Step 3: We consider the new divisor 221 and the new remainder 91, and apply the division lemma to get
221 = 91 x 2 + 39
We consider the new divisor 91 and the new remainder 39,and apply the division lemma to get
91 = 39 x 2 + 13
We consider the new divisor 39 and the new remainder 13,and apply the division lemma to get
39 = 13 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 312 and 845 is 13
Notice that 13 = HCF(39,13) = HCF(91,39) = HCF(221,91) = HCF(312,221) = HCF(845,312) .
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, 845?
Answer: HCF of 312, 845 is 13 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 845 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 845 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.