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 290, 745, 621, 312 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 290, 745, 621, 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 290, 745, 621, 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 290, 745, 621, 312 is 1.
HCF(290, 745, 621, 312) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 290, 745, 621, 312 is 1.
Step 1: Since 745 > 290, we apply the division lemma to 745 and 290, to get
745 = 290 x 2 + 165
Step 2: Since the reminder 290 ≠ 0, we apply division lemma to 165 and 290, to get
290 = 165 x 1 + 125
Step 3: We consider the new divisor 165 and the new remainder 125, and apply the division lemma to get
165 = 125 x 1 + 40
We consider the new divisor 125 and the new remainder 40,and apply the division lemma to get
125 = 40 x 3 + 5
We consider the new divisor 40 and the new remainder 5,and apply the division lemma to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 290 and 745 is 5
Notice that 5 = HCF(40,5) = HCF(125,40) = HCF(165,125) = HCF(290,165) = HCF(745,290) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 621 > 5, we apply the division lemma to 621 and 5, to get
621 = 5 x 124 + 1
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 1 and 5, to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 621 is 1
Notice that 1 = HCF(5,1) = HCF(621,5) .
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 290, 745, 621, 312?
Answer: HCF of 290, 745, 621, 312 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 290, 745, 621, 312 using Euclid's Algorithm?
Answer: For arbitrary numbers 290, 745, 621, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.