Highest Common Factor of 741, 456, 832 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, 456, 832 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 741, 456, 832 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 741, 456, 832 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, 456, 832 is 1.
HCF(741, 456, 832) = 1
HCF of 741, 456, 832 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, 456, 832 is 1.
Highest Common Factor of 741,456,832 is 1
Step 1: Since 741 > 456, we apply the division lemma to 741 and 456, to get
741 = 456 x 1 + 285
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 285 and 456, to get
456 = 285 x 1 + 171
Step 3: We consider the new divisor 285 and the new remainder 171, and apply the division lemma to get
285 = 171 x 1 + 114
We consider the new divisor 171 and the new remainder 114,and apply the division lemma to get
171 = 114 x 1 + 57
We consider the new divisor 114 and the new remainder 57,and apply the division lemma to get
114 = 57 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 57, the HCF of 741 and 456 is 57
Notice that 57 = HCF(114,57) = HCF(171,114) = HCF(285,171) = HCF(456,285) = HCF(741,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 832 > 57, we apply the division lemma to 832 and 57, to get
832 = 57 x 14 + 34
Step 2: Since the reminder 57 ≠ 0, we apply division lemma to 34 and 57, to get
57 = 34 x 1 + 23
Step 3: We consider the new divisor 34 and the new remainder 23, and apply the division lemma to get
34 = 23 x 1 + 11
We consider the new divisor 23 and the new remainder 11,and apply the division lemma to get
23 = 11 x 2 + 1
We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 57 and 832 is 1
Notice that 1 = HCF(11,1) = HCF(23,11) = HCF(34,23) = HCF(57,34) = HCF(832,57) .
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Frequently Asked Questions on HCF of 741, 456, 832 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, 456, 832?
Answer: HCF of 741, 456, 832 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 741, 456, 832 using Euclid's Algorithm?
Answer: For arbitrary numbers 741, 456, 832 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.