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 391, 666, 741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 391, 666, 741 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 391, 666, 741 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 391, 666, 741 is 1.
HCF(391, 666, 741) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 391, 666, 741 is 1.
Step 1: Since 666 > 391, we apply the division lemma to 666 and 391, to get
666 = 391 x 1 + 275
Step 2: Since the reminder 391 ≠ 0, we apply division lemma to 275 and 391, to get
391 = 275 x 1 + 116
Step 3: We consider the new divisor 275 and the new remainder 116, and apply the division lemma to get
275 = 116 x 2 + 43
We consider the new divisor 116 and the new remainder 43,and apply the division lemma to get
116 = 43 x 2 + 30
We consider the new divisor 43 and the new remainder 30,and apply the division lemma to get
43 = 30 x 1 + 13
We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get
30 = 13 x 2 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 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 391 and 666 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(43,30) = HCF(116,43) = HCF(275,116) = HCF(391,275) = HCF(666,391) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 741 > 1, we apply the division lemma to 741 and 1, to get
741 = 1 x 741 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 741 is 1
Notice that 1 = HCF(741,1) .
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 391, 666, 741?
Answer: HCF of 391, 666, 741 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 391, 666, 741 using Euclid's Algorithm?
Answer: For arbitrary numbers 391, 666, 741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.