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 440, 674, 48 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 440, 674, 48 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 440, 674, 48 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 440, 674, 48 is 2.
HCF(440, 674, 48) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 440, 674, 48 is 2.
Step 1: Since 674 > 440, we apply the division lemma to 674 and 440, to get
674 = 440 x 1 + 234
Step 2: Since the reminder 440 ≠ 0, we apply division lemma to 234 and 440, to get
440 = 234 x 1 + 206
Step 3: We consider the new divisor 234 and the new remainder 206, and apply the division lemma to get
234 = 206 x 1 + 28
We consider the new divisor 206 and the new remainder 28,and apply the division lemma to get
206 = 28 x 7 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 440 and 674 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(206,28) = HCF(234,206) = HCF(440,234) = HCF(674,440) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 48 > 2, we apply the division lemma to 48 and 2, to get
48 = 2 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 48 is 2
Notice that 2 = HCF(48,2) .
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 440, 674, 48?
Answer: HCF of 440, 674, 48 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 440, 674, 48 using Euclid's Algorithm?
Answer: For arbitrary numbers 440, 674, 48 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.