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 283, 744, 137 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 283, 744, 137 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 283, 744, 137 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 283, 744, 137 is 1.
HCF(283, 744, 137) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 283, 744, 137 is 1.
Step 1: Since 744 > 283, we apply the division lemma to 744 and 283, to get
744 = 283 x 2 + 178
Step 2: Since the reminder 283 ≠ 0, we apply division lemma to 178 and 283, to get
283 = 178 x 1 + 105
Step 3: We consider the new divisor 178 and the new remainder 105, and apply the division lemma to get
178 = 105 x 1 + 73
We consider the new divisor 105 and the new remainder 73,and apply the division lemma to get
105 = 73 x 1 + 32
We consider the new divisor 73 and the new remainder 32,and apply the division lemma to get
73 = 32 x 2 + 9
We consider the new divisor 32 and the new remainder 9,and apply the division lemma to get
32 = 9 x 3 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 283 and 744 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(32,9) = HCF(73,32) = HCF(105,73) = HCF(178,105) = HCF(283,178) = HCF(744,283) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 137 > 1, we apply the division lemma to 137 and 1, to get
137 = 1 x 137 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 137 is 1
Notice that 1 = HCF(137,1) .
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 283, 744, 137?
Answer: HCF of 283, 744, 137 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 283, 744, 137 using Euclid's Algorithm?
Answer: For arbitrary numbers 283, 744, 137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.