Highest Common Factor of 96, 160, 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 96, 160, 741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 96, 160, 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 96, 160, 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 96, 160, 741 is 1.
HCF(96, 160, 741) = 1
HCF of 96, 160, 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 96, 160, 741 is 1.
Highest Common Factor of 96,160,741 is 1
Step 1: Since 160 > 96, we apply the division lemma to 160 and 96, to get
160 = 96 x 1 + 64
Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 64 and 96, to get
96 = 64 x 1 + 32
Step 3: We consider the new divisor 64 and the new remainder 32, and apply the division lemma to get
64 = 32 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 32, the HCF of 96 and 160 is 32
Notice that 32 = HCF(64,32) = HCF(96,64) = HCF(160,96) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 741 > 32, we apply the division lemma to 741 and 32, to get
741 = 32 x 23 + 5
Step 2: Since the reminder 32 ≠ 0, we apply division lemma to 5 and 32, to get
32 = 5 x 6 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 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 32 and 741 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(32,5) = HCF(741,32) .
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Frequently Asked Questions on HCF of 96, 160, 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 96, 160, 741?
Answer: HCF of 96, 160, 741 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 96, 160, 741 using Euclid's Algorithm?
Answer: For arbitrary numbers 96, 160, 741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.