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 745, 903, 988 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 745, 903, 988 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 745, 903, 988 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 745, 903, 988 is 1.
HCF(745, 903, 988) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 745, 903, 988 is 1.
Step 1: Since 903 > 745, we apply the division lemma to 903 and 745, to get
903 = 745 x 1 + 158
Step 2: Since the reminder 745 ≠ 0, we apply division lemma to 158 and 745, to get
745 = 158 x 4 + 113
Step 3: We consider the new divisor 158 and the new remainder 113, and apply the division lemma to get
158 = 113 x 1 + 45
We consider the new divisor 113 and the new remainder 45,and apply the division lemma to get
113 = 45 x 2 + 23
We consider the new divisor 45 and the new remainder 23,and apply the division lemma to get
45 = 23 x 1 + 22
We consider the new divisor 23 and the new remainder 22,and apply the division lemma to get
23 = 22 x 1 + 1
We consider the new divisor 22 and the new remainder 1,and apply the division lemma to get
22 = 1 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 745 and 903 is 1
Notice that 1 = HCF(22,1) = HCF(23,22) = HCF(45,23) = HCF(113,45) = HCF(158,113) = HCF(745,158) = HCF(903,745) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 988 > 1, we apply the division lemma to 988 and 1, to get
988 = 1 x 988 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 988 is 1
Notice that 1 = HCF(988,1) .
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 745, 903, 988?
Answer: HCF of 745, 903, 988 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 745, 903, 988 using Euclid's Algorithm?
Answer: For arbitrary numbers 745, 903, 988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.