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 870, 270, 780 i.e. 30 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 270, 780 is 30 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 870, 270, 780 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 870, 270, 780 is 30.
HCF(870, 270, 780) = 30
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 870, 270, 780 is 30.
Step 1: Since 870 > 270, we apply the division lemma to 870 and 270, to get
870 = 270 x 3 + 60
Step 2: Since the reminder 270 ≠ 0, we apply division lemma to 60 and 270, to get
270 = 60 x 4 + 30
Step 3: We consider the new divisor 60 and the new remainder 30, and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 870 and 270 is 30
Notice that 30 = HCF(60,30) = HCF(270,60) = HCF(870,270) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 780 > 30, we apply the division lemma to 780 and 30, to get
780 = 30 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 30 and 780 is 30
Notice that 30 = HCF(780,30) .
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 870, 270, 780?
Answer: HCF of 870, 270, 780 is 30 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 270, 780 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 270, 780 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.