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 978, 339, 749 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 978, 339, 749 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 978, 339, 749 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 978, 339, 749 is 1.
HCF(978, 339, 749) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 978, 339, 749 is 1.
Step 1: Since 978 > 339, we apply the division lemma to 978 and 339, to get
978 = 339 x 2 + 300
Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 300 and 339, to get
339 = 300 x 1 + 39
Step 3: We consider the new divisor 300 and the new remainder 39, and apply the division lemma to get
300 = 39 x 7 + 27
We consider the new divisor 39 and the new remainder 27,and apply the division lemma to get
39 = 27 x 1 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 978 and 339 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(39,27) = HCF(300,39) = HCF(339,300) = HCF(978,339) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 749 > 3, we apply the division lemma to 749 and 3, to get
749 = 3 x 249 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 749 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(749,3) .
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 978, 339, 749?
Answer: HCF of 978, 339, 749 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 978, 339, 749 using Euclid's Algorithm?
Answer: For arbitrary numbers 978, 339, 749 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.