Highest Common Factor of 753, 882, 107 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 753, 882, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 753, 882, 107 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 753, 882, 107 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 753, 882, 107 is 1.
HCF(753, 882, 107) = 1
HCF of 753, 882, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 753, 882, 107 is 1.
Highest Common Factor of 753,882,107 is 1
Step 1: Since 882 > 753, we apply the division lemma to 882 and 753, to get
882 = 753 x 1 + 129
Step 2: Since the reminder 753 ≠ 0, we apply division lemma to 129 and 753, to get
753 = 129 x 5 + 108
Step 3: We consider the new divisor 129 and the new remainder 108, and apply the division lemma to get
129 = 108 x 1 + 21
We consider the new divisor 108 and the new remainder 21,and apply the division lemma to get
108 = 21 x 5 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 753 and 882 is 3
Notice that 3 = HCF(21,3) = HCF(108,21) = HCF(129,108) = HCF(753,129) = HCF(882,753) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 3, we apply the division lemma to 107 and 3, to get
107 = 3 x 35 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 107 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(107,3) .
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Frequently Asked Questions on HCF of 753, 882, 107 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 753, 882, 107?
Answer: HCF of 753, 882, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 753, 882, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 753, 882, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.