Highest Common Factor of 333, 777, 141 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 333, 777, 141 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 333, 777, 141 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 333, 777, 141 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 333, 777, 141 is 3.
HCF(333, 777, 141) = 3
HCF of 333, 777, 141 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 333, 777, 141 is 3.
Highest Common Factor of 333,777,141 is 3
Step 1: Since 777 > 333, we apply the division lemma to 777 and 333, to get
777 = 333 x 2 + 111
Step 2: Since the reminder 333 ≠ 0, we apply division lemma to 111 and 333, to get
333 = 111 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 111, the HCF of 333 and 777 is 111
Notice that 111 = HCF(333,111) = HCF(777,333) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 141 > 111, we apply the division lemma to 141 and 111, to get
141 = 111 x 1 + 30
Step 2: Since the reminder 111 ≠ 0, we apply division lemma to 30 and 111, to get
111 = 30 x 3 + 21
Step 3: We consider the new divisor 30 and the new remainder 21, and apply the division lemma to get
30 = 21 x 1 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 111 and 141 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(30,21) = HCF(111,30) = HCF(141,111) .
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Frequently Asked Questions on HCF of 333, 777, 141 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 333, 777, 141?
Answer: HCF of 333, 777, 141 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 333, 777, 141 using Euclid's Algorithm?
Answer: For arbitrary numbers 333, 777, 141 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.