Highest Common Factor of 304, 736, 741 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 304, 736, 741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 304, 736, 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 304, 736, 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 304, 736, 741 is 1.
HCF(304, 736, 741) = 1
HCF of 304, 736, 741 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 304, 736, 741 is 1.
Highest Common Factor of 304,736,741 is 1
Step 1: Since 736 > 304, we apply the division lemma to 736 and 304, to get
736 = 304 x 2 + 128
Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 128 and 304, to get
304 = 128 x 2 + 48
Step 3: We consider the new divisor 128 and the new remainder 48, and apply the division lemma to get
128 = 48 x 2 + 32
We consider the new divisor 48 and the new remainder 32,and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16,and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 304 and 736 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(128,48) = HCF(304,128) = HCF(736,304) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 741 > 16, we apply the division lemma to 741 and 16, to get
741 = 16 x 46 + 5
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 5 and 16, to get
16 = 5 x 3 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 16 and 741 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(741,16) .
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Frequently Asked Questions on HCF of 304, 736, 741 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 304, 736, 741?
Answer: HCF of 304, 736, 741 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 304, 736, 741 using Euclid's Algorithm?
Answer: For arbitrary numbers 304, 736, 741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.