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 930, 510, 18 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 930, 510, 18 is 6 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 930, 510, 18 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 930, 510, 18 is 6.
HCF(930, 510, 18) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 930, 510, 18 is 6.
Step 1: Since 930 > 510, we apply the division lemma to 930 and 510, to get
930 = 510 x 1 + 420
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 420 and 510, to get
510 = 420 x 1 + 90
Step 3: We consider the new divisor 420 and the new remainder 90, and apply the division lemma to get
420 = 90 x 4 + 60
We consider the new divisor 90 and the new remainder 60,and apply the division lemma to get
90 = 60 x 1 + 30
We consider the new divisor 60 and the new remainder 30,and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 930 and 510 is 30
Notice that 30 = HCF(60,30) = HCF(90,60) = HCF(420,90) = HCF(510,420) = HCF(930,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 30 > 18, we apply the division lemma to 30 and 18, to get
30 = 18 x 1 + 12
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 12 and 18, to get
18 = 12 x 1 + 6
Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 18 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) .
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 930, 510, 18?
Answer: HCF of 930, 510, 18 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 930, 510, 18 using Euclid's Algorithm?
Answer: For arbitrary numbers 930, 510, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.