Highest Common Factor of 413, 708 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, 708 i.e. 59 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 708 is 59 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, 708 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, 708 is 59.
HCF(413, 708) = 59
HCF of 413, 708 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, 708 is 59.
Highest Common Factor of 413,708 is 59
Step 1: Since 708 > 413, we apply the division lemma to 708 and 413, to get
708 = 413 x 1 + 295
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 295 and 413, to get
413 = 295 x 1 + 118
Step 3: We consider the new divisor 295 and the new remainder 118, and apply the division lemma to get
295 = 118 x 2 + 59
We consider the new divisor 118 and the new remainder 59, and apply the division lemma to get
118 = 59 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 59, the HCF of 413 and 708 is 59
Notice that 59 = HCF(118,59) = HCF(295,118) = HCF(413,295) = HCF(708,413) .
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Frequently Asked Questions on HCF of 413, 708 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, 708?
Answer: HCF of 413, 708 is 59 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 708 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 708 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.