Highest Common Factor of 754, 169, 112 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, 169, 112 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 754, 169, 112 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, 169, 112 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, 169, 112 is 1.
HCF(754, 169, 112) = 1
HCF of 754, 169, 112 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, 169, 112 is 1.
Highest Common Factor of 754,169,112 is 1
Step 1: Since 754 > 169, we apply the division lemma to 754 and 169, to get
754 = 169 x 4 + 78
Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 78 and 169, to get
169 = 78 x 2 + 13
Step 3: We consider the new divisor 78 and the new remainder 13, and apply the division lemma to get
78 = 13 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 754 and 169 is 13
Notice that 13 = HCF(78,13) = HCF(169,78) = HCF(754,169) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 112 > 13, we apply the division lemma to 112 and 13, to get
112 = 13 x 8 + 8
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 8 and 13, to get
13 = 8 x 1 + 5
Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 13 and 112 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(112,13) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 754, 169, 112 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, 169, 112?
Answer: HCF of 754, 169, 112 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 754, 169, 112 using Euclid's Algorithm?
Answer: For arbitrary numbers 754, 169, 112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.