Highest Common Factor of 408, 975, 901 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 408, 975, 901 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 975, 901 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 408, 975, 901 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 408, 975, 901 is 1.
HCF(408, 975, 901) = 1
HCF of 408, 975, 901 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 975, 901 is 1.
Highest Common Factor of 408,975,901 is 1
Step 1: Since 975 > 408, we apply the division lemma to 975 and 408, to get
975 = 408 x 2 + 159
Step 2: Since the reminder 408 ≠ 0, we apply division lemma to 159 and 408, to get
408 = 159 x 2 + 90
Step 3: We consider the new divisor 159 and the new remainder 90, and apply the division lemma to get
159 = 90 x 1 + 69
We consider the new divisor 90 and the new remainder 69,and apply the division lemma to get
90 = 69 x 1 + 21
We consider the new divisor 69 and the new remainder 21,and apply the division lemma to get
69 = 21 x 3 + 6
We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get
21 = 6 x 3 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 408 and 975 is 3
Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(69,21) = HCF(90,69) = HCF(159,90) = HCF(408,159) = HCF(975,408) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 901 > 3, we apply the division lemma to 901 and 3, to get
901 = 3 x 300 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 901 is 1
Notice that 1 = HCF(3,1) = HCF(901,3) .
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Frequently Asked Questions on HCF of 408, 975, 901 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 408, 975, 901?
Answer: HCF of 408, 975, 901 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 975, 901 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 975, 901 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
