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 559, 344, 442 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 559, 344, 442 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 559, 344, 442 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 559, 344, 442 is 1.
HCF(559, 344, 442) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 559, 344, 442 is 1.
Step 1: Since 559 > 344, we apply the division lemma to 559 and 344, to get
559 = 344 x 1 + 215
Step 2: Since the reminder 344 ≠ 0, we apply division lemma to 215 and 344, to get
344 = 215 x 1 + 129
Step 3: We consider the new divisor 215 and the new remainder 129, and apply the division lemma to get
215 = 129 x 1 + 86
We consider the new divisor 129 and the new remainder 86,and apply the division lemma to get
129 = 86 x 1 + 43
We consider the new divisor 86 and the new remainder 43,and apply the division lemma to get
86 = 43 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 559 and 344 is 43
Notice that 43 = HCF(86,43) = HCF(129,86) = HCF(215,129) = HCF(344,215) = HCF(559,344) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 442 > 43, we apply the division lemma to 442 and 43, to get
442 = 43 x 10 + 12
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 12 and 43, to get
43 = 12 x 3 + 7
Step 3: We consider the new divisor 12 and the new remainder 7, and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 442 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(43,12) = HCF(442,43) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 559, 344, 442?
Answer: HCF of 559, 344, 442 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 559, 344, 442 using Euclid's Algorithm?
Answer: For arbitrary numbers 559, 344, 442 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.