Highest Common Factor of 8757, 345 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 8757, 345 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 8757, 345 is 3 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 8757, 345 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 8757, 345 is 3.
HCF(8757, 345) = 3
HCF of 8757, 345 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8757, 345 is 3.
Highest Common Factor of 8757,345 is 3
Step 1: Since 8757 > 345, we apply the division lemma to 8757 and 345, to get
8757 = 345 x 25 + 132
Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 132 and 345, to get
345 = 132 x 2 + 81
Step 3: We consider the new divisor 132 and the new remainder 81, and apply the division lemma to get
132 = 81 x 1 + 51
We consider the new divisor 81 and the new remainder 51,and apply the division lemma to get
81 = 51 x 1 + 30
We consider the new divisor 51 and the new remainder 30,and apply the division lemma to get
51 = 30 x 1 + 21
We consider the new divisor 30 and the new remainder 21,and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 8757 and 345 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(51,30) = HCF(81,51) = HCF(132,81) = HCF(345,132) = HCF(8757,345) .
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Frequently Asked Questions on HCF of 8757, 345 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 8757, 345?
Answer: HCF of 8757, 345 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8757, 345 using Euclid's Algorithm?
Answer: For arbitrary numbers 8757, 345 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.