Highest Common Factor of 440, 360, 109 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, 360, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 360, 109 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 440, 360, 109 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, 360, 109 is 1.
HCF(440, 360, 109) = 1
HCF of 440, 360, 109 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, 360, 109 is 1.
Highest Common Factor of 440,360,109 is 1
Step 1: Since 440 > 360, we apply the division lemma to 440 and 360, to get
440 = 360 x 1 + 80
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 80 and 360, to get
360 = 80 x 4 + 40
Step 3: We consider the new divisor 80 and the new remainder 40, and apply the division lemma to get
80 = 40 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 440 and 360 is 40
Notice that 40 = HCF(80,40) = HCF(360,80) = HCF(440,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 40, we apply the division lemma to 109 and 40, to get
109 = 40 x 2 + 29
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 29 and 40, to get
40 = 29 x 1 + 11
Step 3: We consider the new divisor 29 and the new remainder 11, and apply the division lemma to get
29 = 11 x 2 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 40 and 109 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(29,11) = HCF(40,29) = HCF(109,40) .
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Frequently Asked Questions on HCF of 440, 360, 109 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, 360, 109?
Answer: HCF of 440, 360, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 360, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 360, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
