Highest Common Factor of 754, 870, 913 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 754, 870, 913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 870, 913 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 754, 870, 913 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 754, 870, 913 is 1.
HCF(754, 870, 913) = 1
HCF of 754, 870, 913 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 754, 870, 913 is 1.
Highest Common Factor of 754,870,913 is 1
Step 1: Since 870 > 754, we apply the division lemma to 870 and 754, to get
870 = 754 x 1 + 116
Step 2: Since the reminder 754 ≠ 0, we apply division lemma to 116 and 754, to get
754 = 116 x 6 + 58
Step 3: We consider the new divisor 116 and the new remainder 58, and apply the division lemma to get
116 = 58 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 58, the HCF of 754 and 870 is 58
Notice that 58 = HCF(116,58) = HCF(754,116) = HCF(870,754) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 913 > 58, we apply the division lemma to 913 and 58, to get
913 = 58 x 15 + 43
Step 2: Since the reminder 58 ≠ 0, we apply division lemma to 43 and 58, to get
58 = 43 x 1 + 15
Step 3: We consider the new divisor 43 and the new remainder 15, and apply the division lemma to get
43 = 15 x 2 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 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 58 and 913 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(58,43) = HCF(913,58) .
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Frequently Asked Questions on HCF of 754, 870, 913 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 754, 870, 913?
Answer: HCF of 754, 870, 913 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 870, 913 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 870, 913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.