Highest Common Factor of 740, 280, 116 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 740, 280, 116 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 740, 280, 116 is 4 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 740, 280, 116 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 740, 280, 116 is 4.
HCF(740, 280, 116) = 4
HCF of 740, 280, 116 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 740, 280, 116 is 4.
Highest Common Factor of 740,280,116 is 4
Step 1: Since 740 > 280, we apply the division lemma to 740 and 280, to get
740 = 280 x 2 + 180
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 180 and 280, to get
280 = 180 x 1 + 100
Step 3: We consider the new divisor 180 and the new remainder 100, and apply the division lemma to get
180 = 100 x 1 + 80
We consider the new divisor 100 and the new remainder 80,and apply the division lemma to get
100 = 80 x 1 + 20
We consider the new divisor 80 and the new remainder 20,and apply the division lemma to get
80 = 20 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 740 and 280 is 20
Notice that 20 = HCF(80,20) = HCF(100,80) = HCF(180,100) = HCF(280,180) = HCF(740,280) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 20, we apply the division lemma to 116 and 20, to get
116 = 20 x 5 + 16
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 16 and 20, to get
20 = 16 x 1 + 4
Step 3: We consider the new divisor 16 and the new remainder 4, and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 116 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(116,20) .
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Frequently Asked Questions on HCF of 740, 280, 116 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 740, 280, 116?
Answer: HCF of 740, 280, 116 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 740, 280, 116 using Euclid's Algorithm?
Answer: For arbitrary numbers 740, 280, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.