Highest Common Factor of 657, 403, 102, 788 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 657, 403, 102, 788 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 657, 403, 102, 788 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 657, 403, 102, 788 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 657, 403, 102, 788 is 1.
HCF(657, 403, 102, 788) = 1
HCF of 657, 403, 102, 788 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 657, 403, 102, 788 is 1.
Highest Common Factor of 657,403,102,788 is 1
Step 1: Since 657 > 403, we apply the division lemma to 657 and 403, to get
657 = 403 x 1 + 254
Step 2: Since the reminder 403 ≠ 0, we apply division lemma to 254 and 403, to get
403 = 254 x 1 + 149
Step 3: We consider the new divisor 254 and the new remainder 149, and apply the division lemma to get
254 = 149 x 1 + 105
We consider the new divisor 149 and the new remainder 105,and apply the division lemma to get
149 = 105 x 1 + 44
We consider the new divisor 105 and the new remainder 44,and apply the division lemma to get
105 = 44 x 2 + 17
We consider the new divisor 44 and the new remainder 17,and apply the division lemma to get
44 = 17 x 2 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 657 and 403 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(44,17) = HCF(105,44) = HCF(149,105) = HCF(254,149) = HCF(403,254) = HCF(657,403) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 102 > 1, we apply the division lemma to 102 and 1, to get
102 = 1 x 102 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 102 is 1
Notice that 1 = HCF(102,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 788 > 1, we apply the division lemma to 788 and 1, to get
788 = 1 x 788 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 788 is 1
Notice that 1 = HCF(788,1) .
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Frequently Asked Questions on HCF of 657, 403, 102, 788 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 657, 403, 102, 788?
Answer: HCF of 657, 403, 102, 788 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 657, 403, 102, 788 using Euclid's Algorithm?
Answer: For arbitrary numbers 657, 403, 102, 788 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
