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 732, 871, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 732, 871, 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 732, 871, 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 732, 871, 754 is 1.
HCF(732, 871, 754) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 732, 871, 754 is 1.
Step 1: Since 871 > 732, we apply the division lemma to 871 and 732, to get
871 = 732 x 1 + 139
Step 2: Since the reminder 732 ≠ 0, we apply division lemma to 139 and 732, to get
732 = 139 x 5 + 37
Step 3: We consider the new divisor 139 and the new remainder 37, and apply the division lemma to get
139 = 37 x 3 + 28
We consider the new divisor 37 and the new remainder 28,and apply the division lemma to get
37 = 28 x 1 + 9
We consider the new divisor 28 and the new remainder 9,and apply the division lemma to get
28 = 9 x 3 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 732 and 871 is 1
Notice that 1 = HCF(9,1) = HCF(28,9) = HCF(37,28) = HCF(139,37) = HCF(732,139) = HCF(871,732) .
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 732, 871, 754?
Answer: HCF of 732, 871, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 732, 871, 754 using Euclid's Algorithm?
Answer: For arbitrary numbers 732, 871, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.