Highest Common Factor of 741, 665 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, 665 i.e. 19 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 665 is 19 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, 665 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, 665 is 19.
HCF(741, 665) = 19
HCF of 741, 665 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, 665 is 19.
Highest Common Factor of 741,665 is 19
Step 1: Since 741 > 665, we apply the division lemma to 741 and 665, to get
741 = 665 x 1 + 76
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 76 and 665, to get
665 = 76 x 8 + 57
Step 3: We consider the new divisor 76 and the new remainder 57, and apply the division lemma to get
76 = 57 x 1 + 19
We consider the new divisor 57 and the new remainder 19, and apply the division lemma to get
57 = 19 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 741 and 665 is 19
Notice that 19 = HCF(57,19) = HCF(76,57) = HCF(665,76) = HCF(741,665) .
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Frequently Asked Questions on HCF of 741, 665 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, 665?
Answer: HCF of 741, 665 is 19 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 665 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.