Highest Common Factor of 860, 232, 86, 914 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 860, 232, 86, 914 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 860, 232, 86, 914 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 860, 232, 86, 914 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 860, 232, 86, 914 is 2.
HCF(860, 232, 86, 914) = 2
HCF of 860, 232, 86, 914 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 860, 232, 86, 914 is 2.
Highest Common Factor of 860,232,86,914 is 2
Step 1: Since 860 > 232, we apply the division lemma to 860 and 232, to get
860 = 232 x 3 + 164
Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 164 and 232, to get
232 = 164 x 1 + 68
Step 3: We consider the new divisor 164 and the new remainder 68, and apply the division lemma to get
164 = 68 x 2 + 28
We consider the new divisor 68 and the new remainder 28,and apply the division lemma to get
68 = 28 x 2 + 12
We consider the new divisor 28 and the new remainder 12,and apply the division lemma to get
28 = 12 x 2 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 860 and 232 is 4
Notice that 4 = HCF(12,4) = HCF(28,12) = HCF(68,28) = HCF(164,68) = HCF(232,164) = HCF(860,232) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 86 > 4, we apply the division lemma to 86 and 4, to get
86 = 4 x 21 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 86 is 2
Notice that 2 = HCF(4,2) = HCF(86,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 914 > 2, we apply the division lemma to 914 and 2, to get
914 = 2 x 457 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 914 is 2
Notice that 2 = HCF(914,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 860, 232, 86, 914 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 860, 232, 86, 914?
Answer: HCF of 860, 232, 86, 914 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 860, 232, 86, 914 using Euclid's Algorithm?
Answer: For arbitrary numbers 860, 232, 86, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
