Highest Common Factor of 744, 433, 977 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 744, 433, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 744, 433, 977 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 744, 433, 977 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 744, 433, 977 is 1.
HCF(744, 433, 977) = 1
HCF of 744, 433, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 744, 433, 977 is 1.
Highest Common Factor of 744,433,977 is 1
Step 1: Since 744 > 433, we apply the division lemma to 744 and 433, to get
744 = 433 x 1 + 311
Step 2: Since the reminder 433 ≠ 0, we apply division lemma to 311 and 433, to get
433 = 311 x 1 + 122
Step 3: We consider the new divisor 311 and the new remainder 122, and apply the division lemma to get
311 = 122 x 2 + 67
We consider the new divisor 122 and the new remainder 67,and apply the division lemma to get
122 = 67 x 1 + 55
We consider the new divisor 67 and the new remainder 55,and apply the division lemma to get
67 = 55 x 1 + 12
We consider the new divisor 55 and the new remainder 12,and apply the division lemma to get
55 = 12 x 4 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
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 744 and 433 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(55,12) = HCF(67,55) = HCF(122,67) = HCF(311,122) = HCF(433,311) = HCF(744,433) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 977 > 1, we apply the division lemma to 977 and 1, to get
977 = 1 x 977 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 977 is 1
Notice that 1 = HCF(977,1) .
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Frequently Asked Questions on HCF of 744, 433, 977 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 744, 433, 977?
Answer: HCF of 744, 433, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 744, 433, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 744, 433, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.