Highest Common Factor of 507, 885, 45 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, 885, 45 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 507, 885, 45 is 3 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, 885, 45 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, 885, 45 is 3.
HCF(507, 885, 45) = 3
HCF of 507, 885, 45 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, 885, 45 is 3.
Highest Common Factor of 507,885,45 is 3
Step 1: Since 885 > 507, we apply the division lemma to 885 and 507, to get
885 = 507 x 1 + 378
Step 2: Since the reminder 507 ≠ 0, we apply division lemma to 378 and 507, to get
507 = 378 x 1 + 129
Step 3: We consider the new divisor 378 and the new remainder 129, and apply the division lemma to get
378 = 129 x 2 + 120
We consider the new divisor 129 and the new remainder 120,and apply the division lemma to get
129 = 120 x 1 + 9
We consider the new divisor 120 and the new remainder 9,and apply the division lemma to get
120 = 9 x 13 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 507 and 885 is 3
Notice that 3 = HCF(9,3) = HCF(120,9) = HCF(129,120) = HCF(378,129) = HCF(507,378) = HCF(885,507) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 3, we apply the division lemma to 45 and 3, to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 45 is 3
Notice that 3 = HCF(45,3) .
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Frequently Asked Questions on HCF of 507, 885, 45 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, 885, 45?
Answer: HCF of 507, 885, 45 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 507, 885, 45 using Euclid's Algorithm?
Answer: For arbitrary numbers 507, 885, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.