Highest Common Factor of 7078, 1478 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 7078, 1478 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7078, 1478 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 7078, 1478 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 7078, 1478 is 2.
HCF(7078, 1478) = 2
HCF of 7078, 1478 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7078, 1478 is 2.
Highest Common Factor of 7078,1478 is 2
Step 1: Since 7078 > 1478, we apply the division lemma to 7078 and 1478, to get
7078 = 1478 x 4 + 1166
Step 2: Since the reminder 1478 ≠ 0, we apply division lemma to 1166 and 1478, to get
1478 = 1166 x 1 + 312
Step 3: We consider the new divisor 1166 and the new remainder 312, and apply the division lemma to get
1166 = 312 x 3 + 230
We consider the new divisor 312 and the new remainder 230,and apply the division lemma to get
312 = 230 x 1 + 82
We consider the new divisor 230 and the new remainder 82,and apply the division lemma to get
230 = 82 x 2 + 66
We consider the new divisor 82 and the new remainder 66,and apply the division lemma to get
82 = 66 x 1 + 16
We consider the new divisor 66 and the new remainder 16,and apply the division lemma to get
66 = 16 x 4 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 7078 and 1478 is 2
Notice that 2 = HCF(16,2) = HCF(66,16) = HCF(82,66) = HCF(230,82) = HCF(312,230) = HCF(1166,312) = HCF(1478,1166) = HCF(7078,1478) .
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Frequently Asked Questions on HCF of 7078, 1478 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 7078, 1478?
Answer: HCF of 7078, 1478 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7078, 1478 using Euclid's Algorithm?
Answer: For arbitrary numbers 7078, 1478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
