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 428, 744 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 428, 744 is 4 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 428, 744 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 428, 744 is 4.
HCF(428, 744) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 428, 744 is 4.
Step 1: Since 744 > 428, we apply the division lemma to 744 and 428, to get
744 = 428 x 1 + 316
Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 316 and 428, to get
428 = 316 x 1 + 112
Step 3: We consider the new divisor 316 and the new remainder 112, and apply the division lemma to get
316 = 112 x 2 + 92
We consider the new divisor 112 and the new remainder 92,and apply the division lemma to get
112 = 92 x 1 + 20
We consider the new divisor 92 and the new remainder 20,and apply the division lemma to get
92 = 20 x 4 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 428 and 744 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(92,20) = HCF(112,92) = HCF(316,112) = HCF(428,316) = HCF(744,428) .
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 428, 744?
Answer: HCF of 428, 744 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 428, 744 using Euclid's Algorithm?
Answer: For arbitrary numbers 428, 744 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.