Highest Common Factor of 413, 679 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 413, 679 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 679 is 7 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 413, 679 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 413, 679 is 7.
HCF(413, 679) = 7
HCF of 413, 679 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 413, 679 is 7.
Highest Common Factor of 413,679 is 7
Step 1: Since 679 > 413, we apply the division lemma to 679 and 413, to get
679 = 413 x 1 + 266
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 266 and 413, to get
413 = 266 x 1 + 147
Step 3: We consider the new divisor 266 and the new remainder 147, and apply the division lemma to get
266 = 147 x 1 + 119
We consider the new divisor 147 and the new remainder 119,and apply the division lemma to get
147 = 119 x 1 + 28
We consider the new divisor 119 and the new remainder 28,and apply the division lemma to get
119 = 28 x 4 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 413 and 679 is 7
Notice that 7 = HCF(28,7) = HCF(119,28) = HCF(147,119) = HCF(266,147) = HCF(413,266) = HCF(679,413) .
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Frequently Asked Questions on HCF of 413, 679 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 413, 679?
Answer: HCF of 413, 679 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 679 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 679 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.