Highest Common Factor of 407, 1656 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 407, 1656 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 407, 1656 is 1 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 407, 1656 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 407, 1656 is 1.
HCF(407, 1656) = 1
HCF of 407, 1656 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 407, 1656 is 1.
Highest Common Factor of 407,1656 is 1
Step 1: Since 1656 > 407, we apply the division lemma to 1656 and 407, to get
1656 = 407 x 4 + 28
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 28 and 407, to get
407 = 28 x 14 + 15
Step 3: We consider the new divisor 28 and the new remainder 15, and apply the division lemma to get
28 = 15 x 1 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 407 and 1656 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(28,15) = HCF(407,28) = HCF(1656,407) .
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Frequently Asked Questions on HCF of 407, 1656 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 407, 1656?
Answer: HCF of 407, 1656 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 407, 1656 using Euclid's Algorithm?
Answer: For arbitrary numbers 407, 1656 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.