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 174, 977, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 977, 754 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 174, 977, 754 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 174, 977, 754 is 1.
HCF(174, 977, 754) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 174, 977, 754 is 1.
Step 1: Since 977 > 174, we apply the division lemma to 977 and 174, to get
977 = 174 x 5 + 107
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 107 and 174, to get
174 = 107 x 1 + 67
Step 3: We consider the new divisor 107 and the new remainder 67, and apply the division lemma to get
107 = 67 x 1 + 40
We consider the new divisor 67 and the new remainder 40,and apply the division lemma to get
67 = 40 x 1 + 27
We consider the new divisor 40 and the new remainder 27,and apply the division lemma to get
40 = 27 x 1 + 13
We consider the new divisor 27 and the new remainder 13,and apply the division lemma to get
27 = 13 x 2 + 1
We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 174 and 977 is 1
Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(40,27) = HCF(67,40) = HCF(107,67) = HCF(174,107) = HCF(977,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 754 > 1, we apply the division lemma to 754 and 1, to get
754 = 1 x 754 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 754 is 1
Notice that 1 = HCF(754,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 174, 977, 754?
Answer: HCF of 174, 977, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 977, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 977, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.