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 375, 900, 968 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 375, 900, 968 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 375, 900, 968 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 375, 900, 968 is 1.
HCF(375, 900, 968) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 375, 900, 968 is 1.
Step 1: Since 900 > 375, we apply the division lemma to 900 and 375, to get
900 = 375 x 2 + 150
Step 2: Since the reminder 375 ≠ 0, we apply division lemma to 150 and 375, to get
375 = 150 x 2 + 75
Step 3: We consider the new divisor 150 and the new remainder 75, and apply the division lemma to get
150 = 75 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 375 and 900 is 75
Notice that 75 = HCF(150,75) = HCF(375,150) = HCF(900,375) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 968 > 75, we apply the division lemma to 968 and 75, to get
968 = 75 x 12 + 68
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 68 and 75, to get
75 = 68 x 1 + 7
Step 3: We consider the new divisor 68 and the new remainder 7, and apply the division lemma to get
68 = 7 x 9 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 75 and 968 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(68,7) = HCF(75,68) = HCF(968,75) .
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 375, 900, 968?
Answer: HCF of 375, 900, 968 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 375, 900, 968 using Euclid's Algorithm?
Answer: For arbitrary numbers 375, 900, 968 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.