Highest Common Factor of 57, 38, 320 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 57, 38, 320 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 57, 38, 320 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 57, 38, 320 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 57, 38, 320 is 1.
HCF(57, 38, 320) = 1
HCF of 57, 38, 320 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 57, 38, 320 is 1.
Highest Common Factor of 57,38,320 is 1
Step 1: Since 57 > 38, we apply the division lemma to 57 and 38, to get
57 = 38 x 1 + 19
Step 2: Since the reminder 38 ≠ 0, we apply division lemma to 19 and 38, to get
38 = 19 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 57 and 38 is 19
Notice that 19 = HCF(38,19) = HCF(57,38) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 320 > 19, we apply the division lemma to 320 and 19, to get
320 = 19 x 16 + 16
Step 2: Since the reminder 19 ≠ 0, we apply division lemma to 16 and 19, to get
19 = 16 x 1 + 3
Step 3: We consider the new divisor 16 and the new remainder 3, and apply the division lemma to get
16 = 3 x 5 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 19 and 320 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(320,19) .
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Frequently Asked Questions on HCF of 57, 38, 320 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 57, 38, 320?
Answer: HCF of 57, 38, 320 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 57, 38, 320 using Euclid's Algorithm?
Answer: For arbitrary numbers 57, 38, 320 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.