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 648, 412, 360 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 648, 412, 360 is 4 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 648, 412, 360 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 648, 412, 360 is 4.
HCF(648, 412, 360) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 648, 412, 360 is 4.
Step 1: Since 648 > 412, we apply the division lemma to 648 and 412, to get
648 = 412 x 1 + 236
Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 236 and 412, to get
412 = 236 x 1 + 176
Step 3: We consider the new divisor 236 and the new remainder 176, and apply the division lemma to get
236 = 176 x 1 + 60
We consider the new divisor 176 and the new remainder 60,and apply the division lemma to get
176 = 60 x 2 + 56
We consider the new divisor 60 and the new remainder 56,and apply the division lemma to get
60 = 56 x 1 + 4
We consider the new divisor 56 and the new remainder 4,and apply the division lemma to get
56 = 4 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 648 and 412 is 4
Notice that 4 = HCF(56,4) = HCF(60,56) = HCF(176,60) = HCF(236,176) = HCF(412,236) = HCF(648,412) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 360 > 4, we apply the division lemma to 360 and 4, to get
360 = 4 x 90 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 360 is 4
Notice that 4 = HCF(360,4) .
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 648, 412, 360?
Answer: HCF of 648, 412, 360 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 648, 412, 360 using Euclid's Algorithm?
Answer: For arbitrary numbers 648, 412, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.