Highest Common Factor of 830, 7918 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, 7918 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 830, 7918 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, 7918 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, 7918 is 2.
HCF(830, 7918) = 2
HCF of 830, 7918 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, 7918 is 2.
Highest Common Factor of 830,7918 is 2
Step 1: Since 7918 > 830, we apply the division lemma to 7918 and 830, to get
7918 = 830 x 9 + 448
Step 2: Since the reminder 830 ≠ 0, we apply division lemma to 448 and 830, to get
830 = 448 x 1 + 382
Step 3: We consider the new divisor 448 and the new remainder 382, and apply the division lemma to get
448 = 382 x 1 + 66
We consider the new divisor 382 and the new remainder 66,and apply the division lemma to get
382 = 66 x 5 + 52
We consider the new divisor 66 and the new remainder 52,and apply the division lemma to get
66 = 52 x 1 + 14
We consider the new divisor 52 and the new remainder 14,and apply the division lemma to get
52 = 14 x 3 + 10
We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get
14 = 10 x 1 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 830 and 7918 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(52,14) = HCF(66,52) = HCF(382,66) = HCF(448,382) = HCF(830,448) = HCF(7918,830) .
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Frequently Asked Questions on HCF of 830, 7918 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, 7918?
Answer: HCF of 830, 7918 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 830, 7918 using Euclid's Algorithm?
Answer: For arbitrary numbers 830, 7918 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.