Highest Common Factor of 798, 465, 111 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 798, 465, 111 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 798, 465, 111 is 3 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 798, 465, 111 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 798, 465, 111 is 3.
HCF(798, 465, 111) = 3
HCF of 798, 465, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 798, 465, 111 is 3.
Highest Common Factor of 798,465,111 is 3
Step 1: Since 798 > 465, we apply the division lemma to 798 and 465, to get
798 = 465 x 1 + 333
Step 2: Since the reminder 465 ≠ 0, we apply division lemma to 333 and 465, to get
465 = 333 x 1 + 132
Step 3: We consider the new divisor 333 and the new remainder 132, and apply the division lemma to get
333 = 132 x 2 + 69
We consider the new divisor 132 and the new remainder 69,and apply the division lemma to get
132 = 69 x 1 + 63
We consider the new divisor 69 and the new remainder 63,and apply the division lemma to get
69 = 63 x 1 + 6
We consider the new divisor 63 and the new remainder 6,and apply the division lemma to get
63 = 6 x 10 + 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 798 and 465 is 3
Notice that 3 = HCF(6,3) = HCF(63,6) = HCF(69,63) = HCF(132,69) = HCF(333,132) = HCF(465,333) = HCF(798,465) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 3, we apply the division lemma to 111 and 3, to get
111 = 3 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 111 is 3
Notice that 3 = HCF(111,3) .
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Frequently Asked Questions on HCF of 798, 465, 111 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 798, 465, 111?
Answer: HCF of 798, 465, 111 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 798, 465, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 798, 465, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.