Highest Common Factor of 74, 16, 16, 433 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 74, 16, 16, 433 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 74, 16, 16, 433 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 74, 16, 16, 433 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 74, 16, 16, 433 is 1.
HCF(74, 16, 16, 433) = 1
HCF of 74, 16, 16, 433 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 74, 16, 16, 433 is 1.
Highest Common Factor of 74,16,16,433 is 1
Step 1: Since 74 > 16, we apply the division lemma to 74 and 16, to get
74 = 16 x 4 + 10
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 10 and 16, to get
16 = 10 x 1 + 6
Step 3: We consider the new divisor 10 and the new remainder 6, and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 74 and 16 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(74,16) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 16 > 2, we apply the division lemma to 16 and 2, to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 16 is 2
Notice that 2 = HCF(16,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 433 > 2, we apply the division lemma to 433 and 2, to get
433 = 2 x 216 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 433 is 1
Notice that 1 = HCF(2,1) = HCF(433,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 74, 16, 16, 433 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 74, 16, 16, 433?
Answer: HCF of 74, 16, 16, 433 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 74, 16, 16, 433 using Euclid's Algorithm?
Answer: For arbitrary numbers 74, 16, 16, 433 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.