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 180, 288, 390 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 180, 288, 390 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 180, 288, 390 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 180, 288, 390 is 6.
HCF(180, 288, 390) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 180, 288, 390 is 6.
Step 1: Since 288 > 180, we apply the division lemma to 288 and 180, to get
288 = 180 x 1 + 108
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 108 and 180, to get
180 = 108 x 1 + 72
Step 3: We consider the new divisor 108 and the new remainder 72, and apply the division lemma to get
108 = 72 x 1 + 36
We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get
72 = 36 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 180 and 288 is 36
Notice that 36 = HCF(72,36) = HCF(108,72) = HCF(180,108) = HCF(288,180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 390 > 36, we apply the division lemma to 390 and 36, to get
390 = 36 x 10 + 30
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 30 and 36, to get
36 = 30 x 1 + 6
Step 3: We consider the new divisor 30 and the new remainder 6, and apply the division lemma to get
30 = 6 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 36 and 390 is 6
Notice that 6 = HCF(30,6) = HCF(36,30) = HCF(390,36) .
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 180, 288, 390?
Answer: HCF of 180, 288, 390 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 180, 288, 390 using Euclid's Algorithm?
Answer: For arbitrary numbers 180, 288, 390 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.