Highest Common Factor of 1008, 7751 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 1008, 7751 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1008, 7751 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 1008, 7751 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 1008, 7751 is 1.
HCF(1008, 7751) = 1
HCF of 1008, 7751 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1008, 7751 is 1.
Highest Common Factor of 1008,7751 is 1
Step 1: Since 7751 > 1008, we apply the division lemma to 7751 and 1008, to get
7751 = 1008 x 7 + 695
Step 2: Since the reminder 1008 ≠ 0, we apply division lemma to 695 and 1008, to get
1008 = 695 x 1 + 313
Step 3: We consider the new divisor 695 and the new remainder 313, and apply the division lemma to get
695 = 313 x 2 + 69
We consider the new divisor 313 and the new remainder 69,and apply the division lemma to get
313 = 69 x 4 + 37
We consider the new divisor 69 and the new remainder 37,and apply the division lemma to get
69 = 37 x 1 + 32
We consider the new divisor 37 and the new remainder 32,and apply the division lemma to get
37 = 32 x 1 + 5
We consider the new divisor 32 and the new remainder 5,and apply the division lemma to get
32 = 5 x 6 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 1008 and 7751 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(37,32) = HCF(69,37) = HCF(313,69) = HCF(695,313) = HCF(1008,695) = HCF(7751,1008) .
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Frequently Asked Questions on HCF of 1008, 7751 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 1008, 7751?
Answer: HCF of 1008, 7751 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1008, 7751 using Euclid's Algorithm?
Answer: For arbitrary numbers 1008, 7751 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.