Highest Common Factor of 118, 314, 732 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 118, 314, 732 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 118, 314, 732 is 2 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 118, 314, 732 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 118, 314, 732 is 2.
HCF(118, 314, 732) = 2
HCF of 118, 314, 732 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 118, 314, 732 is 2.
Highest Common Factor of 118,314,732 is 2
Step 1: Since 314 > 118, we apply the division lemma to 314 and 118, to get
314 = 118 x 2 + 78
Step 2: Since the reminder 118 ≠ 0, we apply division lemma to 78 and 118, to get
118 = 78 x 1 + 40
Step 3: We consider the new divisor 78 and the new remainder 40, and apply the division lemma to get
78 = 40 x 1 + 38
We consider the new divisor 40 and the new remainder 38,and apply the division lemma to get
40 = 38 x 1 + 2
We consider the new divisor 38 and the new remainder 2,and apply the division lemma to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 118 and 314 is 2
Notice that 2 = HCF(38,2) = HCF(40,38) = HCF(78,40) = HCF(118,78) = HCF(314,118) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 732 > 2, we apply the division lemma to 732 and 2, to get
732 = 2 x 366 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 732 is 2
Notice that 2 = HCF(732,2) .
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Frequently Asked Questions on HCF of 118, 314, 732 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 118, 314, 732?
Answer: HCF of 118, 314, 732 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 118, 314, 732 using Euclid's Algorithm?
Answer: For arbitrary numbers 118, 314, 732 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.