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 398, 632, 516 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 398, 632, 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 398, 632, 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 398, 632, 516 is 2.
HCF(398, 632, 516) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 398, 632, 516 is 2.
Step 1: Since 632 > 398, we apply the division lemma to 632 and 398, to get
632 = 398 x 1 + 234
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 234 and 398, to get
398 = 234 x 1 + 164
Step 3: We consider the new divisor 234 and the new remainder 164, and apply the division lemma to get
234 = 164 x 1 + 70
We consider the new divisor 164 and the new remainder 70,and apply the division lemma to get
164 = 70 x 2 + 24
We consider the new divisor 70 and the new remainder 24,and apply the division lemma to get
70 = 24 x 2 + 22
We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 398 and 632 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(70,24) = HCF(164,70) = HCF(234,164) = HCF(398,234) = HCF(632,398) .
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) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 398, 632, 516?
Answer: HCF of 398, 632, 516 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 398, 632, 516 using Euclid's Algorithm?
Answer: For arbitrary numbers 398, 632, 516 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.