Highest Common Factor of 282, 416, 208 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 282, 416, 208 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 282, 416, 208 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 282, 416, 208 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 282, 416, 208 is 2.
HCF(282, 416, 208) = 2
HCF of 282, 416, 208 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 282, 416, 208 is 2.
Highest Common Factor of 282,416,208 is 2
Step 1: Since 416 > 282, we apply the division lemma to 416 and 282, to get
416 = 282 x 1 + 134
Step 2: Since the reminder 282 ≠ 0, we apply division lemma to 134 and 282, to get
282 = 134 x 2 + 14
Step 3: We consider the new divisor 134 and the new remainder 14, and apply the division lemma to get
134 = 14 x 9 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 282 and 416 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(134,14) = HCF(282,134) = HCF(416,282) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 208 > 2, we apply the division lemma to 208 and 2, to get
208 = 2 x 104 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 208 is 2
Notice that 2 = HCF(208,2) .
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Frequently Asked Questions on HCF of 282, 416, 208 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 282, 416, 208?
Answer: HCF of 282, 416, 208 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 282, 416, 208 using Euclid's Algorithm?
Answer: For arbitrary numbers 282, 416, 208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.