Highest Common Factor of 441, 280, 407 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 441, 280, 407 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 441, 280, 407 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 441, 280, 407 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 441, 280, 407 is 1.
HCF(441, 280, 407) = 1
HCF of 441, 280, 407 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 441, 280, 407 is 1.
Highest Common Factor of 441,280,407 is 1
Step 1: Since 441 > 280, we apply the division lemma to 441 and 280, to get
441 = 280 x 1 + 161
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 161 and 280, to get
280 = 161 x 1 + 119
Step 3: We consider the new divisor 161 and the new remainder 119, and apply the division lemma to get
161 = 119 x 1 + 42
We consider the new divisor 119 and the new remainder 42,and apply the division lemma to get
119 = 42 x 2 + 35
We consider the new divisor 42 and the new remainder 35,and apply the division lemma to get
42 = 35 x 1 + 7
We consider the new divisor 35 and the new remainder 7,and apply the division lemma to get
35 = 7 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 441 and 280 is 7
Notice that 7 = HCF(35,7) = HCF(42,35) = HCF(119,42) = HCF(161,119) = HCF(280,161) = HCF(441,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 407 > 7, we apply the division lemma to 407 and 7, to get
407 = 7 x 58 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 407 is 1
Notice that 1 = HCF(7,1) = HCF(407,7) .
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Frequently Asked Questions on HCF of 441, 280, 407 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 441, 280, 407?
Answer: HCF of 441, 280, 407 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 441, 280, 407 using Euclid's Algorithm?
Answer: For arbitrary numbers 441, 280, 407 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.