Highest Common Factor of 656, 388, 413, 456 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 656, 388, 413, 456 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 656, 388, 413, 456 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 656, 388, 413, 456 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 656, 388, 413, 456 is 1.
HCF(656, 388, 413, 456) = 1
HCF of 656, 388, 413, 456 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 656, 388, 413, 456 is 1.
Highest Common Factor of 656,388,413,456 is 1
Step 1: Since 656 > 388, we apply the division lemma to 656 and 388, to get
656 = 388 x 1 + 268
Step 2: Since the reminder 388 ≠ 0, we apply division lemma to 268 and 388, to get
388 = 268 x 1 + 120
Step 3: We consider the new divisor 268 and the new remainder 120, and apply the division lemma to get
268 = 120 x 2 + 28
We consider the new divisor 120 and the new remainder 28,and apply the division lemma to get
120 = 28 x 4 + 8
We consider the new divisor 28 and the new remainder 8,and apply the division lemma to get
28 = 8 x 3 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 656 and 388 is 4
Notice that 4 = HCF(8,4) = HCF(28,8) = HCF(120,28) = HCF(268,120) = HCF(388,268) = HCF(656,388) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 413 > 4, we apply the division lemma to 413 and 4, to get
413 = 4 x 103 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 413 is 1
Notice that 1 = HCF(4,1) = HCF(413,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 456 > 1, we apply the division lemma to 456 and 1, to get
456 = 1 x 456 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 456 is 1
Notice that 1 = HCF(456,1) .
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Frequently Asked Questions on HCF of 656, 388, 413, 456 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 656, 388, 413, 456?
Answer: HCF of 656, 388, 413, 456 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 656, 388, 413, 456 using Euclid's Algorithm?
Answer: For arbitrary numbers 656, 388, 413, 456 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.