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 810, 705 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 810, 705 is 15 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 810, 705 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 810, 705 is 15.
HCF(810, 705) = 15
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 810, 705 is 15.
Step 1: Since 810 > 705, we apply the division lemma to 810 and 705, to get
810 = 705 x 1 + 105
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 105 and 705, to get
705 = 105 x 6 + 75
Step 3: We consider the new divisor 105 and the new remainder 75, and apply the division lemma to get
105 = 75 x 1 + 30
We consider the new divisor 75 and the new remainder 30,and apply the division lemma to get
75 = 30 x 2 + 15
We consider the new divisor 30 and the new remainder 15,and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 810 and 705 is 15
Notice that 15 = HCF(30,15) = HCF(75,30) = HCF(105,75) = HCF(705,105) = HCF(810,705) .
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 810, 705?
Answer: HCF of 810, 705 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 810, 705 using Euclid's Algorithm?
Answer: For arbitrary numbers 810, 705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.