Highest Common Factor of 507, 8305 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 507, 8305 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 507, 8305 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 507, 8305 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 507, 8305 is 1.
HCF(507, 8305) = 1
HCF of 507, 8305 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 507, 8305 is 1.
Highest Common Factor of 507,8305 is 1
Step 1: Since 8305 > 507, we apply the division lemma to 8305 and 507, to get
8305 = 507 x 16 + 193
Step 2: Since the reminder 507 ≠ 0, we apply division lemma to 193 and 507, to get
507 = 193 x 2 + 121
Step 3: We consider the new divisor 193 and the new remainder 121, and apply the division lemma to get
193 = 121 x 1 + 72
We consider the new divisor 121 and the new remainder 72,and apply the division lemma to get
121 = 72 x 1 + 49
We consider the new divisor 72 and the new remainder 49,and apply the division lemma to get
72 = 49 x 1 + 23
We consider the new divisor 49 and the new remainder 23,and apply the division lemma to get
49 = 23 x 2 + 3
We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get
23 = 3 x 7 + 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 507 and 8305 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(49,23) = HCF(72,49) = HCF(121,72) = HCF(193,121) = HCF(507,193) = HCF(8305,507) .
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Frequently Asked Questions on HCF of 507, 8305 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 507, 8305?
Answer: HCF of 507, 8305 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 507, 8305 using Euclid's Algorithm?
Answer: For arbitrary numbers 507, 8305 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.