Highest Common Factor of 7005, 8522 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, 8522 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7005, 8522 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, 8522 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, 8522 is 1.
HCF(7005, 8522) = 1
HCF of 7005, 8522 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, 8522 is 1.
Highest Common Factor of 7005,8522 is 1
Step 1: Since 8522 > 7005, we apply the division lemma to 8522 and 7005, to get
8522 = 7005 x 1 + 1517
Step 2: Since the reminder 7005 ≠ 0, we apply division lemma to 1517 and 7005, to get
7005 = 1517 x 4 + 937
Step 3: We consider the new divisor 1517 and the new remainder 937, and apply the division lemma to get
1517 = 937 x 1 + 580
We consider the new divisor 937 and the new remainder 580,and apply the division lemma to get
937 = 580 x 1 + 357
We consider the new divisor 580 and the new remainder 357,and apply the division lemma to get
580 = 357 x 1 + 223
We consider the new divisor 357 and the new remainder 223,and apply the division lemma to get
357 = 223 x 1 + 134
We consider the new divisor 223 and the new remainder 134,and apply the division lemma to get
223 = 134 x 1 + 89
We consider the new divisor 134 and the new remainder 89,and apply the division lemma to get
134 = 89 x 1 + 45
We consider the new divisor 89 and the new remainder 45,and apply the division lemma to get
89 = 45 x 1 + 44
We consider the new divisor 45 and the new remainder 44,and apply the division lemma to get
45 = 44 x 1 + 1
We consider the new divisor 44 and the new remainder 1,and apply the division lemma to get
44 = 1 x 44 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7005 and 8522 is 1
Notice that 1 = HCF(44,1) = HCF(45,44) = HCF(89,45) = HCF(134,89) = HCF(223,134) = HCF(357,223) = HCF(580,357) = HCF(937,580) = HCF(1517,937) = HCF(7005,1517) = HCF(8522,7005) .
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Frequently Asked Questions on HCF of 7005, 8522 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, 8522?
Answer: HCF of 7005, 8522 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7005, 8522 using Euclid's Algorithm?
Answer: For arbitrary numbers 7005, 8522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.