Highest Common Factor of 7005, 7748 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 7005, 7748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7005, 7748 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 7005, 7748 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 7005, 7748 is 1.
HCF(7005, 7748) = 1
HCF of 7005, 7748 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7005, 7748 is 1.
Highest Common Factor of 7005,7748 is 1
Step 1: Since 7748 > 7005, we apply the division lemma to 7748 and 7005, to get
7748 = 7005 x 1 + 743
Step 2: Since the reminder 7005 ≠ 0, we apply division lemma to 743 and 7005, to get
7005 = 743 x 9 + 318
Step 3: We consider the new divisor 743 and the new remainder 318, and apply the division lemma to get
743 = 318 x 2 + 107
We consider the new divisor 318 and the new remainder 107,and apply the division lemma to get
318 = 107 x 2 + 104
We consider the new divisor 107 and the new remainder 104,and apply the division lemma to get
107 = 104 x 1 + 3
We consider the new divisor 104 and the new remainder 3,and apply the division lemma to get
104 = 3 x 34 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 7005 and 7748 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(104,3) = HCF(107,104) = HCF(318,107) = HCF(743,318) = HCF(7005,743) = HCF(7748,7005) .
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Frequently Asked Questions on HCF of 7005, 7748 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 7005, 7748?
Answer: HCF of 7005, 7748 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7005, 7748 using Euclid's Algorithm?
Answer: For arbitrary numbers 7005, 7748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.