Highest Common Factor of 782, 322, 258 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 782, 322, 258 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 782, 322, 258 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 782, 322, 258 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 782, 322, 258 is 2.
HCF(782, 322, 258) = 2
HCF of 782, 322, 258 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 782, 322, 258 is 2.
Highest Common Factor of 782,322,258 is 2
Step 1: Since 782 > 322, we apply the division lemma to 782 and 322, to get
782 = 322 x 2 + 138
Step 2: Since the reminder 322 ≠ 0, we apply division lemma to 138 and 322, to get
322 = 138 x 2 + 46
Step 3: We consider the new divisor 138 and the new remainder 46, and apply the division lemma to get
138 = 46 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 46, the HCF of 782 and 322 is 46
Notice that 46 = HCF(138,46) = HCF(322,138) = HCF(782,322) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 258 > 46, we apply the division lemma to 258 and 46, to get
258 = 46 x 5 + 28
Step 2: Since the reminder 46 ≠ 0, we apply division lemma to 28 and 46, to get
46 = 28 x 1 + 18
Step 3: We consider the new divisor 28 and the new remainder 18, and apply the division lemma to get
28 = 18 x 1 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 46 and 258 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(28,18) = HCF(46,28) = HCF(258,46) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 782, 322, 258 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 782, 322, 258?
Answer: HCF of 782, 322, 258 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 782, 322, 258 using Euclid's Algorithm?
Answer: For arbitrary numbers 782, 322, 258 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.