Highest Common Factor of 440, 546 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 440, 546 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 546 is 2 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 440, 546 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 440, 546 is 2.
HCF(440, 546) = 2
HCF of 440, 546 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 440, 546 is 2.
Highest Common Factor of 440,546 is 2
Step 1: Since 546 > 440, we apply the division lemma to 546 and 440, to get
546 = 440 x 1 + 106
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 106 and 440, to get
440 = 106 x 4 + 16
Step 3: We consider the new divisor 106 and the new remainder 16, and apply the division lemma to get
106 = 16 x 6 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
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 440 and 546 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(106,16) = HCF(440,106) = HCF(546,440) .
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Frequently Asked Questions on HCF of 440, 546 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 440, 546?
Answer: HCF of 440, 546 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 546 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.