Highest Common Factor of 390, 105, 256 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, 105, 256 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 390, 105, 256 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 390, 105, 256 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, 105, 256 is 1.
HCF(390, 105, 256) = 1
HCF of 390, 105, 256 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, 105, 256 is 1.
Highest Common Factor of 390,105,256 is 1
Step 1: Since 390 > 105, we apply the division lemma to 390 and 105, to get
390 = 105 x 3 + 75
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 75 and 105, to get
105 = 75 x 1 + 30
Step 3: We consider the new divisor 75 and the new remainder 30, and apply the division lemma to get
75 = 30 x 2 + 15
We consider the new divisor 30 and the new remainder 15, and apply the division lemma to get
30 = 15 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 390 and 105 is 15
Notice that 15 = HCF(30,15) = HCF(75,30) = HCF(105,75) = HCF(390,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 256 > 15, we apply the division lemma to 256 and 15, to get
256 = 15 x 17 + 1
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 1 and 15, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 256 is 1
Notice that 1 = HCF(15,1) = HCF(256,15) .
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Frequently Asked Questions on HCF of 390, 105, 256 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, 105, 256?
Answer: HCF of 390, 105, 256 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 390, 105, 256 using Euclid's Algorithm?
Answer: For arbitrary numbers 390, 105, 256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.