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 310, 283, 456, 768 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 283, 456, 768 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 310, 283, 456, 768 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 310, 283, 456, 768 is 1.
HCF(310, 283, 456, 768) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 283, 456, 768 is 1.
Step 1: Since 310 > 283, we apply the division lemma to 310 and 283, to get
310 = 283 x 1 + 27
Step 2: Since the reminder 283 ≠ 0, we apply division lemma to 27 and 283, to get
283 = 27 x 10 + 13
Step 3: We consider the new divisor 27 and the new remainder 13, and apply the division lemma to get
27 = 13 x 2 + 1
We consider the new divisor 13 and the new remainder 1, and apply the division lemma to get
13 = 1 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 310 and 283 is 1
Notice that 1 = HCF(13,1) = HCF(27,13) = HCF(283,27) = HCF(310,283) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 456 > 1, we apply the division lemma to 456 and 1, to get
456 = 1 x 456 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 456 is 1
Notice that 1 = HCF(456,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 768 > 1, we apply the division lemma to 768 and 1, to get
768 = 1 x 768 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 768 is 1
Notice that 1 = HCF(768,1) .
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 310, 283, 456, 768?
Answer: HCF of 310, 283, 456, 768 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 283, 456, 768 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 283, 456, 768 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.