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 748, 446, 439 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 748, 446, 439 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 748, 446, 439 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 748, 446, 439 is 1.
HCF(748, 446, 439) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 748, 446, 439 is 1.
Step 1: Since 748 > 446, we apply the division lemma to 748 and 446, to get
748 = 446 x 1 + 302
Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 302 and 446, to get
446 = 302 x 1 + 144
Step 3: We consider the new divisor 302 and the new remainder 144, and apply the division lemma to get
302 = 144 x 2 + 14
We consider the new divisor 144 and the new remainder 14,and apply the division lemma to get
144 = 14 x 10 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 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 748 and 446 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(144,14) = HCF(302,144) = HCF(446,302) = HCF(748,446) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 439 > 2, we apply the division lemma to 439 and 2, to get
439 = 2 x 219 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 439 is 1
Notice that 1 = HCF(2,1) = HCF(439,2) .
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 748, 446, 439?
Answer: HCF of 748, 446, 439 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 748, 446, 439 using Euclid's Algorithm?
Answer: For arbitrary numbers 748, 446, 439 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.