Highest Common Factor of 830, 7278 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 830, 7278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 830, 7278 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 830, 7278 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 830, 7278 is 2.
HCF(830, 7278) = 2
HCF of 830, 7278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 830, 7278 is 2.
Highest Common Factor of 830,7278 is 2
Step 1: Since 7278 > 830, we apply the division lemma to 7278 and 830, to get
7278 = 830 x 8 + 638
Step 2: Since the reminder 830 ≠ 0, we apply division lemma to 638 and 830, to get
830 = 638 x 1 + 192
Step 3: We consider the new divisor 638 and the new remainder 192, and apply the division lemma to get
638 = 192 x 3 + 62
We consider the new divisor 192 and the new remainder 62,and apply the division lemma to get
192 = 62 x 3 + 6
We consider the new divisor 62 and the new remainder 6,and apply the division lemma to get
62 = 6 x 10 + 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 830 and 7278 is 2
Notice that 2 = HCF(6,2) = HCF(62,6) = HCF(192,62) = HCF(638,192) = HCF(830,638) = HCF(7278,830) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 830, 7278 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 830, 7278?
Answer: HCF of 830, 7278 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 830, 7278 using Euclid's Algorithm?
Answer: For arbitrary numbers 830, 7278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.