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 407, 782, 312 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 407, 782, 312 is 1 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 407, 782, 312 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 407, 782, 312 is 1.
HCF(407, 782, 312) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 407, 782, 312 is 1.
Step 1: Since 782 > 407, we apply the division lemma to 782 and 407, to get
782 = 407 x 1 + 375
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 375 and 407, to get
407 = 375 x 1 + 32
Step 3: We consider the new divisor 375 and the new remainder 32, and apply the division lemma to get
375 = 32 x 11 + 23
We consider the new divisor 32 and the new remainder 23,and apply the division lemma to get
32 = 23 x 1 + 9
We consider the new divisor 23 and the new remainder 9,and apply the division lemma to get
23 = 9 x 2 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 407 and 782 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(23,9) = HCF(32,23) = HCF(375,32) = HCF(407,375) = HCF(782,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 312 > 1, we apply the division lemma to 312 and 1, to get
312 = 1 x 312 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 312 is 1
Notice that 1 = HCF(312,1) .
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 407, 782, 312?
Answer: HCF of 407, 782, 312 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 407, 782, 312 using Euclid's Algorithm?
Answer: For arbitrary numbers 407, 782, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.