Highest Common Factor of 785, 314, 380 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 785, 314, 380 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 314, 380 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 785, 314, 380 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 785, 314, 380 is 1.
HCF(785, 314, 380) = 1
HCF of 785, 314, 380 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 314, 380 is 1.
Highest Common Factor of 785,314,380 is 1
Step 1: Since 785 > 314, we apply the division lemma to 785 and 314, to get
785 = 314 x 2 + 157
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 157 and 314, to get
314 = 157 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 157, the HCF of 785 and 314 is 157
Notice that 157 = HCF(314,157) = HCF(785,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 380 > 157, we apply the division lemma to 380 and 157, to get
380 = 157 x 2 + 66
Step 2: Since the reminder 157 ≠ 0, we apply division lemma to 66 and 157, to get
157 = 66 x 2 + 25
Step 3: We consider the new divisor 66 and the new remainder 25, and apply the division lemma to get
66 = 25 x 2 + 16
We consider the new divisor 25 and the new remainder 16,and apply the division lemma to get
25 = 16 x 1 + 9
We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get
16 = 9 x 1 + 7
We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get
9 = 7 x 1 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
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 157 and 380 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(25,16) = HCF(66,25) = HCF(157,66) = HCF(380,157) .
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Frequently Asked Questions on HCF of 785, 314, 380 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 785, 314, 380?
Answer: HCF of 785, 314, 380 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 314, 380 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 314, 380 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.