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, 977, 15 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 283, 977, 15 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, 977, 15 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, 977, 15 is 1.
HCF(283, 977, 15) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 283, 977, 15 is 1.
Step 1: Since 977 > 283, we apply the division lemma to 977 and 283, to get
977 = 283 x 3 + 128
Step 2: Since the reminder 283 ≠ 0, we apply division lemma to 128 and 283, to get
283 = 128 x 2 + 27
Step 3: We consider the new divisor 128 and the new remainder 27, and apply the division lemma to get
128 = 27 x 4 + 20
We consider the new divisor 27 and the new remainder 20,and apply the division lemma to get
27 = 20 x 1 + 7
We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get
20 = 7 x 2 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 283 and 977 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(128,27) = HCF(283,128) = HCF(977,283) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 1, we apply the division lemma to 15 and 1, to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 15 is 1
Notice that 1 = HCF(15,1) .
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, 977, 15?
Answer: HCF of 283, 977, 15 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 283, 977, 15 using Euclid's Algorithm?
Answer: For arbitrary numbers 283, 977, 15 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.