Highest Common Factor of 615, 972, 314 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 615, 972, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 615, 972, 314 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 615, 972, 314 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 615, 972, 314 is 1.
HCF(615, 972, 314) = 1
HCF of 615, 972, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 615, 972, 314 is 1.
Highest Common Factor of 615,972,314 is 1
Step 1: Since 972 > 615, we apply the division lemma to 972 and 615, to get
972 = 615 x 1 + 357
Step 2: Since the reminder 615 ≠ 0, we apply division lemma to 357 and 615, to get
615 = 357 x 1 + 258
Step 3: We consider the new divisor 357 and the new remainder 258, and apply the division lemma to get
357 = 258 x 1 + 99
We consider the new divisor 258 and the new remainder 99,and apply the division lemma to get
258 = 99 x 2 + 60
We consider the new divisor 99 and the new remainder 60,and apply the division lemma to get
99 = 60 x 1 + 39
We consider the new divisor 60 and the new remainder 39,and apply the division lemma to get
60 = 39 x 1 + 21
We consider the new divisor 39 and the new remainder 21,and apply the division lemma to get
39 = 21 x 1 + 18
We consider the new divisor 21 and the new remainder 18,and apply the division lemma to get
21 = 18 x 1 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 615 and 972 is 3
Notice that 3 = HCF(18,3) = HCF(21,18) = HCF(39,21) = HCF(60,39) = HCF(99,60) = HCF(258,99) = HCF(357,258) = HCF(615,357) = HCF(972,615) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 3, we apply the division lemma to 314 and 3, to get
314 = 3 x 104 + 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 314 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(314,3) .
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Frequently Asked Questions on HCF of 615, 972, 314 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 615, 972, 314?
Answer: HCF of 615, 972, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 615, 972, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 615, 972, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.