Highest Common Factor of 340, 240, 100 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 340, 240, 100 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 240, 100 is 20 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 340, 240, 100 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 340, 240, 100 is 20.
HCF(340, 240, 100) = 20
HCF of 340, 240, 100 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 240, 100 is 20.
Highest Common Factor of 340,240,100 is 20
Step 1: Since 340 > 240, we apply the division lemma to 340 and 240, to get
340 = 240 x 1 + 100
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 100 and 240, to get
240 = 100 x 2 + 40
Step 3: We consider the new divisor 100 and the new remainder 40, and apply the division lemma to get
100 = 40 x 2 + 20
We consider the new divisor 40 and the new remainder 20, and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 340 and 240 is 20
Notice that 20 = HCF(40,20) = HCF(100,40) = HCF(240,100) = HCF(340,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 100 > 20, we apply the division lemma to 100 and 20, to get
100 = 20 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 20 and 100 is 20
Notice that 20 = HCF(100,20) .
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Frequently Asked Questions on HCF of 340, 240, 100 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 340, 240, 100?
Answer: HCF of 340, 240, 100 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 240, 100 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 240, 100 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.