Highest Common Factor of 454, 280, 449, 42 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 454, 280, 449, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 454, 280, 449, 42 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 454, 280, 449, 42 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 454, 280, 449, 42 is 1.
HCF(454, 280, 449, 42) = 1
HCF of 454, 280, 449, 42 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 454, 280, 449, 42 is 1.
Highest Common Factor of 454,280,449,42 is 1
Step 1: Since 454 > 280, we apply the division lemma to 454 and 280, to get
454 = 280 x 1 + 174
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 174 and 280, to get
280 = 174 x 1 + 106
Step 3: We consider the new divisor 174 and the new remainder 106, and apply the division lemma to get
174 = 106 x 1 + 68
We consider the new divisor 106 and the new remainder 68,and apply the division lemma to get
106 = 68 x 1 + 38
We consider the new divisor 68 and the new remainder 38,and apply the division lemma to get
68 = 38 x 1 + 30
We consider the new divisor 38 and the new remainder 30,and apply the division lemma to get
38 = 30 x 1 + 8
We consider the new divisor 30 and the new remainder 8,and apply the division lemma to get
30 = 8 x 3 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 454 and 280 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(30,8) = HCF(38,30) = HCF(68,38) = HCF(106,68) = HCF(174,106) = HCF(280,174) = HCF(454,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 449 > 2, we apply the division lemma to 449 and 2, to get
449 = 2 x 224 + 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 449 is 1
Notice that 1 = HCF(2,1) = HCF(449,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 454, 280, 449, 42 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 454, 280, 449, 42?
Answer: HCF of 454, 280, 449, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 454, 280, 449, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 454, 280, 449, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.