Highest Common Factor of 390, 615, 42, 507 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 390, 615, 42, 507 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 390, 615, 42, 507 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 390, 615, 42, 507 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 390, 615, 42, 507 is 3.
HCF(390, 615, 42, 507) = 3
HCF of 390, 615, 42, 507 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 390, 615, 42, 507 is 3.
Highest Common Factor of 390,615,42,507 is 3
Step 1: Since 615 > 390, we apply the division lemma to 615 and 390, to get
615 = 390 x 1 + 225
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 225 and 390, to get
390 = 225 x 1 + 165
Step 3: We consider the new divisor 225 and the new remainder 165, and apply the division lemma to get
225 = 165 x 1 + 60
We consider the new divisor 165 and the new remainder 60,and apply the division lemma to get
165 = 60 x 2 + 45
We consider the new divisor 60 and the new remainder 45,and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 390 and 615 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(165,60) = HCF(225,165) = HCF(390,225) = HCF(615,390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 15, we apply the division lemma to 42 and 15, to get
42 = 15 x 2 + 12
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 12 and 15, to get
15 = 12 x 1 + 3
Step 3: We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 42 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(42,15) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 507 > 3, we apply the division lemma to 507 and 3, to get
507 = 3 x 169 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 507 is 3
Notice that 3 = HCF(507,3) .
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Frequently Asked Questions on HCF of 390, 615, 42, 507 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 390, 615, 42, 507?
Answer: HCF of 390, 615, 42, 507 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 390, 615, 42, 507 using Euclid's Algorithm?
Answer: For arbitrary numbers 390, 615, 42, 507 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.