Highest Common Factor of 628, 6142 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 628, 6142 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 628, 6142 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 628, 6142 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 628, 6142 is 2.
HCF(628, 6142) = 2
HCF of 628, 6142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 628, 6142 is 2.
Highest Common Factor of 628,6142 is 2
Step 1: Since 6142 > 628, we apply the division lemma to 6142 and 628, to get
6142 = 628 x 9 + 490
Step 2: Since the reminder 628 ≠ 0, we apply division lemma to 490 and 628, to get
628 = 490 x 1 + 138
Step 3: We consider the new divisor 490 and the new remainder 138, and apply the division lemma to get
490 = 138 x 3 + 76
We consider the new divisor 138 and the new remainder 76,and apply the division lemma to get
138 = 76 x 1 + 62
We consider the new divisor 76 and the new remainder 62,and apply the division lemma to get
76 = 62 x 1 + 14
We consider the new divisor 62 and the new remainder 14,and apply the division lemma to get
62 = 14 x 4 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 628 and 6142 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(62,14) = HCF(76,62) = HCF(138,76) = HCF(490,138) = HCF(628,490) = HCF(6142,628) .
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Frequently Asked Questions on HCF of 628, 6142 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 628, 6142?
Answer: HCF of 628, 6142 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 628, 6142 using Euclid's Algorithm?
Answer: For arbitrary numbers 628, 6142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.