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 445, 712, 390 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 445, 712, 390 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 445, 712, 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 445, 712, 390 is 1.
HCF(445, 712, 390) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 445, 712, 390 is 1.
Step 1: Since 712 > 445, we apply the division lemma to 712 and 445, to get
712 = 445 x 1 + 267
Step 2: Since the reminder 445 ≠ 0, we apply division lemma to 267 and 445, to get
445 = 267 x 1 + 178
Step 3: We consider the new divisor 267 and the new remainder 178, and apply the division lemma to get
267 = 178 x 1 + 89
We consider the new divisor 178 and the new remainder 89, and apply the division lemma to get
178 = 89 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 89, the HCF of 445 and 712 is 89
Notice that 89 = HCF(178,89) = HCF(267,178) = HCF(445,267) = HCF(712,445) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 390 > 89, we apply the division lemma to 390 and 89, to get
390 = 89 x 4 + 34
Step 2: Since the reminder 89 ≠ 0, we apply division lemma to 34 and 89, to get
89 = 34 x 2 + 21
Step 3: We consider the new divisor 34 and the new remainder 21, and apply the division lemma to get
34 = 21 x 1 + 13
We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get
21 = 13 x 1 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 89 and 390 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(34,21) = HCF(89,34) = HCF(390,89) .
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 445, 712, 390?
Answer: HCF of 445, 712, 390 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 445, 712, 390 using Euclid's Algorithm?
Answer: For arbitrary numbers 445, 712, 390 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.