Highest Common Factor of 781, 731, 456 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 781, 731, 456 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 781, 731, 456 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 781, 731, 456 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 781, 731, 456 is 1.
HCF(781, 731, 456) = 1
HCF of 781, 731, 456 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 781, 731, 456 is 1.
Highest Common Factor of 781,731,456 is 1
Step 1: Since 781 > 731, we apply the division lemma to 781 and 731, to get
781 = 731 x 1 + 50
Step 2: Since the reminder 731 ≠ 0, we apply division lemma to 50 and 731, to get
731 = 50 x 14 + 31
Step 3: We consider the new divisor 50 and the new remainder 31, and apply the division lemma to get
50 = 31 x 1 + 19
We consider the new divisor 31 and the new remainder 19,and apply the division lemma to get
31 = 19 x 1 + 12
We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get
19 = 12 x 1 + 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 781 and 731 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(31,19) = HCF(50,31) = HCF(731,50) = HCF(781,731) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 456 > 1, we apply the division lemma to 456 and 1, to get
456 = 1 x 456 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 456 is 1
Notice that 1 = HCF(456,1) .
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Frequently Asked Questions on HCF of 781, 731, 456 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 781, 731, 456?
Answer: HCF of 781, 731, 456 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 781, 731, 456 using Euclid's Algorithm?
Answer: For arbitrary numbers 781, 731, 456 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.