Highest Common Factor of 433, 312, 105 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 433, 312, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 433, 312, 105 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 433, 312, 105 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 433, 312, 105 is 1.
HCF(433, 312, 105) = 1
HCF of 433, 312, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 433, 312, 105 is 1.
Highest Common Factor of 433,312,105 is 1
Step 1: Since 433 > 312, we apply the division lemma to 433 and 312, to get
433 = 312 x 1 + 121
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 121 and 312, to get
312 = 121 x 2 + 70
Step 3: We consider the new divisor 121 and the new remainder 70, and apply the division lemma to get
121 = 70 x 1 + 51
We consider the new divisor 70 and the new remainder 51,and apply the division lemma to get
70 = 51 x 1 + 19
We consider the new divisor 51 and the new remainder 19,and apply the division lemma to get
51 = 19 x 2 + 13
We consider the new divisor 19 and the new remainder 13,and apply the division lemma to get
19 = 13 x 1 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 433 and 312 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(19,13) = HCF(51,19) = HCF(70,51) = HCF(121,70) = HCF(312,121) = HCF(433,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
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Frequently Asked Questions on HCF of 433, 312, 105 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 433, 312, 105?
Answer: HCF of 433, 312, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 433, 312, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 433, 312, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
