Highest Common Factor of 2278, 1730 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 2278, 1730 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 2278, 1730 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 2278, 1730 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 2278, 1730 is 2.
HCF(2278, 1730) = 2
HCF of 2278, 1730 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2278, 1730 is 2.
Highest Common Factor of 2278,1730 is 2
Step 1: Since 2278 > 1730, we apply the division lemma to 2278 and 1730, to get
2278 = 1730 x 1 + 548
Step 2: Since the reminder 1730 ≠ 0, we apply division lemma to 548 and 1730, to get
1730 = 548 x 3 + 86
Step 3: We consider the new divisor 548 and the new remainder 86, and apply the division lemma to get
548 = 86 x 6 + 32
We consider the new divisor 86 and the new remainder 32,and apply the division lemma to get
86 = 32 x 2 + 22
We consider the new divisor 32 and the new remainder 22,and apply the division lemma to get
32 = 22 x 1 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2278 and 1730 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(32,22) = HCF(86,32) = HCF(548,86) = HCF(1730,548) = HCF(2278,1730) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2278, 1730 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 2278, 1730?
Answer: HCF of 2278, 1730 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2278, 1730 using Euclid's Algorithm?
Answer: For arbitrary numbers 2278, 1730 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.