Highest Common Factor of 504, 311, 744, 66 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 504, 311, 744, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 504, 311, 744, 66 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 504, 311, 744, 66 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 504, 311, 744, 66 is 1.
HCF(504, 311, 744, 66) = 1
HCF of 504, 311, 744, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 504, 311, 744, 66 is 1.
Highest Common Factor of 504,311,744,66 is 1
Step 1: Since 504 > 311, we apply the division lemma to 504 and 311, to get
504 = 311 x 1 + 193
Step 2: Since the reminder 311 ≠ 0, we apply division lemma to 193 and 311, to get
311 = 193 x 1 + 118
Step 3: We consider the new divisor 193 and the new remainder 118, and apply the division lemma to get
193 = 118 x 1 + 75
We consider the new divisor 118 and the new remainder 75,and apply the division lemma to get
118 = 75 x 1 + 43
We consider the new divisor 75 and the new remainder 43,and apply the division lemma to get
75 = 43 x 1 + 32
We consider the new divisor 43 and the new remainder 32,and apply the division lemma to get
43 = 32 x 1 + 11
We consider the new divisor 32 and the new remainder 11,and apply the division lemma to get
32 = 11 x 2 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 504 and 311 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(32,11) = HCF(43,32) = HCF(75,43) = HCF(118,75) = HCF(193,118) = HCF(311,193) = HCF(504,311) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 744 > 1, we apply the division lemma to 744 and 1, to get
744 = 1 x 744 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 744 is 1
Notice that 1 = HCF(744,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get
66 = 1 x 66 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1
Notice that 1 = HCF(66,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 504, 311, 744, 66 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 504, 311, 744, 66?
Answer: HCF of 504, 311, 744, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 504, 311, 744, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 504, 311, 744, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.