Highest Common Factor of 372, 998, 516 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 372, 998, 516 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 372, 998, 516 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 372, 998, 516 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 372, 998, 516 is 2.
HCF(372, 998, 516) = 2
HCF of 372, 998, 516 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 372, 998, 516 is 2.
Highest Common Factor of 372,998,516 is 2
Step 1: Since 998 > 372, we apply the division lemma to 998 and 372, to get
998 = 372 x 2 + 254
Step 2: Since the reminder 372 ≠ 0, we apply division lemma to 254 and 372, to get
372 = 254 x 1 + 118
Step 3: We consider the new divisor 254 and the new remainder 118, and apply the division lemma to get
254 = 118 x 2 + 18
We consider the new divisor 118 and the new remainder 18,and apply the division lemma to get
118 = 18 x 6 + 10
We consider the new divisor 18 and the new remainder 10,and apply the division lemma to get
18 = 10 x 1 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 372 and 998 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18,10) = HCF(118,18) = HCF(254,118) = HCF(372,254) = HCF(998,372) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 516 > 2, we apply the division lemma to 516 and 2, to get
516 = 2 x 258 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 516 is 2
Notice that 2 = HCF(516,2) .
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Frequently Asked Questions on HCF of 372, 998, 516 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 372, 998, 516?
Answer: HCF of 372, 998, 516 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 372, 998, 516 using Euclid's Algorithm?
Answer: For arbitrary numbers 372, 998, 516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.