Highest Common Factor of 741, 207 using Euclid's algorithm
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 741, 207 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 207 is 3 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 741, 207 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 741, 207 is 3.
HCF(741, 207) = 3
HCF of 741, 207 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 741, 207 is 3.
Highest Common Factor of 741,207 is 3
Step 1: Since 741 > 207, we apply the division lemma to 741 and 207, to get
741 = 207 x 3 + 120
Step 2: Since the reminder 207 ≠ 0, we apply division lemma to 120 and 207, to get
207 = 120 x 1 + 87
Step 3: We consider the new divisor 120 and the new remainder 87, and apply the division lemma to get
120 = 87 x 1 + 33
We consider the new divisor 87 and the new remainder 33,and apply the division lemma to get
87 = 33 x 2 + 21
We consider the new divisor 33 and the new remainder 21,and apply the division lemma to get
33 = 21 x 1 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 741 and 207 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(33,21) = HCF(87,33) = HCF(120,87) = HCF(207,120) = HCF(741,207) .
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Frequently Asked Questions on HCF of 741, 207 using Euclid's Algorithm
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 741, 207?
Answer: HCF of 741, 207 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 207 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 207 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.