Highest Common Factor of 457, 2106 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 457, 2106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 457, 2106 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 457, 2106 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 457, 2106 is 1.
HCF(457, 2106) = 1
HCF of 457, 2106 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 457, 2106 is 1.
Highest Common Factor of 457,2106 is 1
Step 1: Since 2106 > 457, we apply the division lemma to 2106 and 457, to get
2106 = 457 x 4 + 278
Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 278 and 457, to get
457 = 278 x 1 + 179
Step 3: We consider the new divisor 278 and the new remainder 179, and apply the division lemma to get
278 = 179 x 1 + 99
We consider the new divisor 179 and the new remainder 99,and apply the division lemma to get
179 = 99 x 1 + 80
We consider the new divisor 99 and the new remainder 80,and apply the division lemma to get
99 = 80 x 1 + 19
We consider the new divisor 80 and the new remainder 19,and apply the division lemma to get
80 = 19 x 4 + 4
We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get
19 = 4 x 4 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 2106 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(80,19) = HCF(99,80) = HCF(179,99) = HCF(278,179) = HCF(457,278) = HCF(2106,457) .
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Frequently Asked Questions on HCF of 457, 2106 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 457, 2106?
Answer: HCF of 457, 2106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 457, 2106 using Euclid's Algorithm?
Answer: For arbitrary numbers 457, 2106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
