Highest Common Factor of 314, 537, 368, 16 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 314, 537, 368, 16 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 537, 368, 16 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 314, 537, 368, 16 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 314, 537, 368, 16 is 1.
HCF(314, 537, 368, 16) = 1
HCF of 314, 537, 368, 16 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 314, 537, 368, 16 is 1.
Highest Common Factor of 314,537,368,16 is 1
Step 1: Since 537 > 314, we apply the division lemma to 537 and 314, to get
537 = 314 x 1 + 223
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 223 and 314, to get
314 = 223 x 1 + 91
Step 3: We consider the new divisor 223 and the new remainder 91, and apply the division lemma to get
223 = 91 x 2 + 41
We consider the new divisor 91 and the new remainder 41,and apply the division lemma to get
91 = 41 x 2 + 9
We consider the new divisor 41 and the new remainder 9,and apply the division lemma to get
41 = 9 x 4 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 314 and 537 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(41,9) = HCF(91,41) = HCF(223,91) = HCF(314,223) = HCF(537,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 368 > 1, we apply the division lemma to 368 and 1, to get
368 = 1 x 368 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 368 is 1
Notice that 1 = HCF(368,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 1, we apply the division lemma to 16 and 1, to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 16 is 1
Notice that 1 = HCF(16,1) .
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Frequently Asked Questions on HCF of 314, 537, 368, 16 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 314, 537, 368, 16?
Answer: HCF of 314, 537, 368, 16 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 537, 368, 16 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 537, 368, 16 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.