Highest Common Factor of 315, 438, 68 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 315, 438, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 438, 68 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 315, 438, 68 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 315, 438, 68 is 1.
HCF(315, 438, 68) = 1
HCF of 315, 438, 68 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 315, 438, 68 is 1.
Highest Common Factor of 315,438,68 is 1
Step 1: Since 438 > 315, we apply the division lemma to 438 and 315, to get
438 = 315 x 1 + 123
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 123 and 315, to get
315 = 123 x 2 + 69
Step 3: We consider the new divisor 123 and the new remainder 69, and apply the division lemma to get
123 = 69 x 1 + 54
We consider the new divisor 69 and the new remainder 54,and apply the division lemma to get
69 = 54 x 1 + 15
We consider the new divisor 54 and the new remainder 15,and apply the division lemma to get
54 = 15 x 3 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 315 and 438 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(54,15) = HCF(69,54) = HCF(123,69) = HCF(315,123) = HCF(438,315) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 3, we apply the division lemma to 68 and 3, to get
68 = 3 x 22 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 68 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(68,3) .
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Frequently Asked Questions on HCF of 315, 438, 68 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 315, 438, 68?
Answer: HCF of 315, 438, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 438, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 438, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.