Highest Common Factor of 8008, 1751 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 8008, 1751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8008, 1751 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 8008, 1751 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 8008, 1751 is 1.
HCF(8008, 1751) = 1
HCF of 8008, 1751 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8008, 1751 is 1.
Highest Common Factor of 8008,1751 is 1
Step 1: Since 8008 > 1751, we apply the division lemma to 8008 and 1751, to get
8008 = 1751 x 4 + 1004
Step 2: Since the reminder 1751 ≠ 0, we apply division lemma to 1004 and 1751, to get
1751 = 1004 x 1 + 747
Step 3: We consider the new divisor 1004 and the new remainder 747, and apply the division lemma to get
1004 = 747 x 1 + 257
We consider the new divisor 747 and the new remainder 257,and apply the division lemma to get
747 = 257 x 2 + 233
We consider the new divisor 257 and the new remainder 233,and apply the division lemma to get
257 = 233 x 1 + 24
We consider the new divisor 233 and the new remainder 24,and apply the division lemma to get
233 = 24 x 9 + 17
We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get
24 = 17 x 1 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 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 8008 and 1751 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(233,24) = HCF(257,233) = HCF(747,257) = HCF(1004,747) = HCF(1751,1004) = HCF(8008,1751) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 8008, 1751 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 8008, 1751?
Answer: HCF of 8008, 1751 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8008, 1751 using Euclid's Algorithm?
Answer: For arbitrary numbers 8008, 1751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.