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 360, 807, 18 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 807, 18 is 3 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 360, 807, 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 360, 807, 18 is 3.
HCF(360, 807, 18) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 807, 18 is 3.
Step 1: Since 807 > 360, we apply the division lemma to 807 and 360, to get
807 = 360 x 2 + 87
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 87 and 360, to get
360 = 87 x 4 + 12
Step 3: We consider the new divisor 87 and the new remainder 12, and apply the division lemma to get
87 = 12 x 7 + 3
We consider the new divisor 12 and the new remainder 3, and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 360 and 807 is 3
Notice that 3 = HCF(12,3) = HCF(87,12) = HCF(360,87) = HCF(807,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18 > 3, we apply the division lemma to 18 and 3, to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 18 is 3
Notice that 3 = HCF(18,3) .
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 360, 807, 18?
Answer: HCF of 360, 807, 18 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 807, 18 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 807, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.