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, 564, 540 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 398, 564, 540 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, 564, 540 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, 564, 540 is 2.
HCF(398, 564, 540) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 398, 564, 540 is 2.
Step 1: Since 564 > 398, we apply the division lemma to 564 and 398, to get
564 = 398 x 1 + 166
Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 166 and 398, to get
398 = 166 x 2 + 66
Step 3: We consider the new divisor 166 and the new remainder 66, and apply the division lemma to get
166 = 66 x 2 + 34
We consider the new divisor 66 and the new remainder 34,and apply the division lemma to get
66 = 34 x 1 + 32
We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 398 and 564 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(66,34) = HCF(166,66) = HCF(398,166) = HCF(564,398) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 540 > 2, we apply the division lemma to 540 and 2, to get
540 = 2 x 270 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 540 is 2
Notice that 2 = HCF(540,2) .
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, 564, 540?
Answer: HCF of 398, 564, 540 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 398, 564, 540 using Euclid's Algorithm?
Answer: For arbitrary numbers 398, 564, 540 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.