Highest Common Factor of 975, 440, 403 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 975, 440, 403 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 975, 440, 403 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 975, 440, 403 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 975, 440, 403 is 1.
HCF(975, 440, 403) = 1
HCF of 975, 440, 403 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 975, 440, 403 is 1.
Highest Common Factor of 975,440,403 is 1
Step 1: Since 975 > 440, we apply the division lemma to 975 and 440, to get
975 = 440 x 2 + 95
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 95 and 440, to get
440 = 95 x 4 + 60
Step 3: We consider the new divisor 95 and the new remainder 60, and apply the division lemma to get
95 = 60 x 1 + 35
We consider the new divisor 60 and the new remainder 35,and apply the division lemma to get
60 = 35 x 1 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 975 and 440 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) = HCF(95,60) = HCF(440,95) = HCF(975,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 403 > 5, we apply the division lemma to 403 and 5, to get
403 = 5 x 80 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: 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 5 and 403 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(403,5) .
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Frequently Asked Questions on HCF of 975, 440, 403 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 975, 440, 403?
Answer: HCF of 975, 440, 403 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 975, 440, 403 using Euclid's Algorithm?
Answer: For arbitrary numbers 975, 440, 403 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.