Highest Common Factor of 86, 338, 870 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 86, 338, 870 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 86, 338, 870 is 2 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 86, 338, 870 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 86, 338, 870 is 2.
HCF(86, 338, 870) = 2
HCF of 86, 338, 870 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 86, 338, 870 is 2.
Highest Common Factor of 86,338,870 is 2
Step 1: Since 338 > 86, we apply the division lemma to 338 and 86, to get
338 = 86 x 3 + 80
Step 2: Since the reminder 86 ≠ 0, we apply division lemma to 80 and 86, to get
86 = 80 x 1 + 6
Step 3: We consider the new divisor 80 and the new remainder 6, and apply the division lemma to get
80 = 6 x 13 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 86 and 338 is 2
Notice that 2 = HCF(6,2) = HCF(80,6) = HCF(86,80) = HCF(338,86) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 870 > 2, we apply the division lemma to 870 and 2, to get
870 = 2 x 435 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 870 is 2
Notice that 2 = HCF(870,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 86, 338, 870 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 86, 338, 870?
Answer: HCF of 86, 338, 870 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 86, 338, 870 using Euclid's Algorithm?
Answer: For arbitrary numbers 86, 338, 870 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.