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 552, 982, 310 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 552, 982, 310 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 552, 982, 310 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 552, 982, 310 is 2.
HCF(552, 982, 310) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 552, 982, 310 is 2.
Step 1: Since 982 > 552, we apply the division lemma to 982 and 552, to get
982 = 552 x 1 + 430
Step 2: Since the reminder 552 ≠ 0, we apply division lemma to 430 and 552, to get
552 = 430 x 1 + 122
Step 3: We consider the new divisor 430 and the new remainder 122, and apply the division lemma to get
430 = 122 x 3 + 64
We consider the new divisor 122 and the new remainder 64,and apply the division lemma to get
122 = 64 x 1 + 58
We consider the new divisor 64 and the new remainder 58,and apply the division lemma to get
64 = 58 x 1 + 6
We consider the new divisor 58 and the new remainder 6,and apply the division lemma to get
58 = 6 x 9 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 552 and 982 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(58,6) = HCF(64,58) = HCF(122,64) = HCF(430,122) = HCF(552,430) = HCF(982,552) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 310 > 2, we apply the division lemma to 310 and 2, to get
310 = 2 x 155 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 310 is 2
Notice that 2 = HCF(310,2) .
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 552, 982, 310?
Answer: HCF of 552, 982, 310 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 552, 982, 310 using Euclid's Algorithm?
Answer: For arbitrary numbers 552, 982, 310 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.