Highest Common Factor of 736, 1605 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 736, 1605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 736, 1605 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 736, 1605 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 736, 1605 is 1.
HCF(736, 1605) = 1
HCF of 736, 1605 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 736, 1605 is 1.
Highest Common Factor of 736,1605 is 1
Step 1: Since 1605 > 736, we apply the division lemma to 1605 and 736, to get
1605 = 736 x 2 + 133
Step 2: Since the reminder 736 ≠ 0, we apply division lemma to 133 and 736, to get
736 = 133 x 5 + 71
Step 3: We consider the new divisor 133 and the new remainder 71, and apply the division lemma to get
133 = 71 x 1 + 62
We consider the new divisor 71 and the new remainder 62,and apply the division lemma to get
71 = 62 x 1 + 9
We consider the new divisor 62 and the new remainder 9,and apply the division lemma to get
62 = 9 x 6 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 736 and 1605 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(62,9) = HCF(71,62) = HCF(133,71) = HCF(736,133) = HCF(1605,736) .
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Frequently Asked Questions on HCF of 736, 1605 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 736, 1605?
Answer: HCF of 736, 1605 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 736, 1605 using Euclid's Algorithm?
Answer: For arbitrary numbers 736, 1605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.