Highest Common Factor of 107, 173, 103, 782 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 107, 173, 103, 782 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 107, 173, 103, 782 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 107, 173, 103, 782 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 107, 173, 103, 782 is 1.
HCF(107, 173, 103, 782) = 1
HCF of 107, 173, 103, 782 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 107, 173, 103, 782 is 1.
Highest Common Factor of 107,173,103,782 is 1
Step 1: Since 173 > 107, we apply the division lemma to 173 and 107, to get
173 = 107 x 1 + 66
Step 2: Since the reminder 107 ≠ 0, we apply division lemma to 66 and 107, to get
107 = 66 x 1 + 41
Step 3: We consider the new divisor 66 and the new remainder 41, and apply the division lemma to get
66 = 41 x 1 + 25
We consider the new divisor 41 and the new remainder 25,and apply the division lemma to get
41 = 25 x 1 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 107 and 173 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(41,25) = HCF(66,41) = HCF(107,66) = HCF(173,107) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 103 > 1, we apply the division lemma to 103 and 1, to get
103 = 1 x 103 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 103 is 1
Notice that 1 = HCF(103,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 782 > 1, we apply the division lemma to 782 and 1, to get
782 = 1 x 782 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 782 is 1
Notice that 1 = HCF(782,1) .
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Frequently Asked Questions on HCF of 107, 173, 103, 782 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 107, 173, 103, 782?
Answer: HCF of 107, 173, 103, 782 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 107, 173, 103, 782 using Euclid's Algorithm?
Answer: For arbitrary numbers 107, 173, 103, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.