Highest Common Factor of 402, 7178 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 402, 7178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 402, 7178 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 402, 7178 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 402, 7178 is 2.
HCF(402, 7178) = 2
HCF of 402, 7178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 402, 7178 is 2.
Highest Common Factor of 402,7178 is 2
Step 1: Since 7178 > 402, we apply the division lemma to 7178 and 402, to get
7178 = 402 x 17 + 344
Step 2: Since the reminder 402 ≠ 0, we apply division lemma to 344 and 402, to get
402 = 344 x 1 + 58
Step 3: We consider the new divisor 344 and the new remainder 58, and apply the division lemma to get
344 = 58 x 5 + 54
We consider the new divisor 58 and the new remainder 54,and apply the division lemma to get
58 = 54 x 1 + 4
We consider the new divisor 54 and the new remainder 4,and apply the division lemma to get
54 = 4 x 13 + 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 402 and 7178 is 2
Notice that 2 = HCF(4,2) = HCF(54,4) = HCF(58,54) = HCF(344,58) = HCF(402,344) = HCF(7178,402) .
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Frequently Asked Questions on HCF of 402, 7178 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 402, 7178?
Answer: HCF of 402, 7178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 402, 7178 using Euclid's Algorithm?
Answer: For arbitrary numbers 402, 7178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.