Highest Common Factor of 340, 200, 299, 105 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, 200, 299, 105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 200, 299, 105 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 340, 200, 299, 105 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, 200, 299, 105 is 1.
HCF(340, 200, 299, 105) = 1
HCF of 340, 200, 299, 105 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, 200, 299, 105 is 1.
Highest Common Factor of 340,200,299,105 is 1
Step 1: Since 340 > 200, we apply the division lemma to 340 and 200, to get
340 = 200 x 1 + 140
Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 140 and 200, to get
200 = 140 x 1 + 60
Step 3: We consider the new divisor 140 and the new remainder 60, and apply the division lemma to get
140 = 60 x 2 + 20
We consider the new divisor 60 and the new remainder 20, and apply the division lemma to get
60 = 20 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 340 and 200 is 20
Notice that 20 = HCF(60,20) = HCF(140,60) = HCF(200,140) = HCF(340,200) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 299 > 20, we apply the division lemma to 299 and 20, to get
299 = 20 x 14 + 19
Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 19 and 20, to get
20 = 19 x 1 + 1
Step 3: We consider the new divisor 19 and the new remainder 1, and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 20 and 299 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(299,20) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 105 > 1, we apply the division lemma to 105 and 1, to get
105 = 1 x 105 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 105 is 1
Notice that 1 = HCF(105,1) .
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Frequently Asked Questions on HCF of 340, 200, 299, 105 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, 200, 299, 105?
Answer: HCF of 340, 200, 299, 105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 200, 299, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 200, 299, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.