Highest Common Factor of 870, 631, 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 870, 631, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 870, 631, 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 870, 631, 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 870, 631, 314 is 1.
HCF(870, 631, 314) = 1
HCF of 870, 631, 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 870, 631, 314 is 1.
Highest Common Factor of 870,631,314 is 1
Step 1: Since 870 > 631, we apply the division lemma to 870 and 631, to get
870 = 631 x 1 + 239
Step 2: Since the reminder 631 ≠ 0, we apply division lemma to 239 and 631, to get
631 = 239 x 2 + 153
Step 3: We consider the new divisor 239 and the new remainder 153, and apply the division lemma to get
239 = 153 x 1 + 86
We consider the new divisor 153 and the new remainder 86,and apply the division lemma to get
153 = 86 x 1 + 67
We consider the new divisor 86 and the new remainder 67,and apply the division lemma to get
86 = 67 x 1 + 19
We consider the new divisor 67 and the new remainder 19,and apply the division lemma to get
67 = 19 x 3 + 10
We consider the new divisor 19 and the new remainder 10,and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 870 and 631 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(67,19) = HCF(86,67) = HCF(153,86) = HCF(239,153) = HCF(631,239) = HCF(870,631) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 1, we apply the division lemma to 314 and 1, to get
314 = 1 x 314 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 314 is 1
Notice that 1 = HCF(314,1) .
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Frequently Asked Questions on HCF of 870, 631, 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 870, 631, 314?
Answer: HCF of 870, 631, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 870, 631, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 870, 631, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.