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 3412, 741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3412, 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 3412, 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 3412, 741 is 1.
HCF(3412, 741) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3412, 741 is 1.
Step 1: Since 3412 > 741, we apply the division lemma to 3412 and 741, to get
3412 = 741 x 4 + 448
Step 2: Since the reminder 741 ≠ 0, we apply division lemma to 448 and 741, to get
741 = 448 x 1 + 293
Step 3: We consider the new divisor 448 and the new remainder 293, and apply the division lemma to get
448 = 293 x 1 + 155
We consider the new divisor 293 and the new remainder 155,and apply the division lemma to get
293 = 155 x 1 + 138
We consider the new divisor 155 and the new remainder 138,and apply the division lemma to get
155 = 138 x 1 + 17
We consider the new divisor 138 and the new remainder 17,and apply the division lemma to get
138 = 17 x 8 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 3412 and 741 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(138,17) = HCF(155,138) = HCF(293,155) = HCF(448,293) = HCF(741,448) = HCF(3412,741) .
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 3412, 741?
Answer: HCF of 3412, 741 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3412, 741 using Euclid's Algorithm?
Answer: For arbitrary numbers 3412, 741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.