Highest Common Factor of 400, 557, 460 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 400, 557, 460 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 400, 557, 460 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 400, 557, 460 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 400, 557, 460 is 1.
HCF(400, 557, 460) = 1
HCF of 400, 557, 460 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 400, 557, 460 is 1.
Highest Common Factor of 400,557,460 is 1
Step 1: Since 557 > 400, we apply the division lemma to 557 and 400, to get
557 = 400 x 1 + 157
Step 2: Since the reminder 400 ≠ 0, we apply division lemma to 157 and 400, to get
400 = 157 x 2 + 86
Step 3: We consider the new divisor 157 and the new remainder 86, and apply the division lemma to get
157 = 86 x 1 + 71
We consider the new divisor 86 and the new remainder 71,and apply the division lemma to get
86 = 71 x 1 + 15
We consider the new divisor 71 and the new remainder 15,and apply the division lemma to get
71 = 15 x 4 + 11
We consider the new divisor 15 and the new remainder 11,and apply the division lemma to get
15 = 11 x 1 + 4
We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get
11 = 4 x 2 + 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 400 and 557 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(15,11) = HCF(71,15) = HCF(86,71) = HCF(157,86) = HCF(400,157) = HCF(557,400) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 460 > 1, we apply the division lemma to 460 and 1, to get
460 = 1 x 460 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 460 is 1
Notice that 1 = HCF(460,1) .
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Frequently Asked Questions on HCF of 400, 557, 460 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 400, 557, 460?
Answer: HCF of 400, 557, 460 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 400, 557, 460 using Euclid's Algorithm?
Answer: For arbitrary numbers 400, 557, 460 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
