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 732, 7218, 4226 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 732, 7218, 4226 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 732, 7218, 4226 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 732, 7218, 4226 is 2.
HCF(732, 7218, 4226) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 732, 7218, 4226 is 2.
Step 1: Since 7218 > 732, we apply the division lemma to 7218 and 732, to get
7218 = 732 x 9 + 630
Step 2: Since the reminder 732 ≠ 0, we apply division lemma to 630 and 732, to get
732 = 630 x 1 + 102
Step 3: We consider the new divisor 630 and the new remainder 102, and apply the division lemma to get
630 = 102 x 6 + 18
We consider the new divisor 102 and the new remainder 18,and apply the division lemma to get
102 = 18 x 5 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
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 732 and 7218 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(102,18) = HCF(630,102) = HCF(732,630) = HCF(7218,732) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4226 > 6, we apply the division lemma to 4226 and 6, to get
4226 = 6 x 704 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 4226 is 2
Notice that 2 = HCF(6,2) = HCF(4226,6) .
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 732, 7218, 4226?
Answer: HCF of 732, 7218, 4226 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 732, 7218, 4226 using Euclid's Algorithm?
Answer: For arbitrary numbers 732, 7218, 4226 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.