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 432, 64, 743, 531 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 64, 743, 531 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 432, 64, 743, 531 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 432, 64, 743, 531 is 1.
HCF(432, 64, 743, 531) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 432, 64, 743, 531 is 1.
Step 1: Since 432 > 64, we apply the division lemma to 432 and 64, to get
432 = 64 x 6 + 48
Step 2: Since the reminder 64 ≠ 0, we apply division lemma to 48 and 64, to get
64 = 48 x 1 + 16
Step 3: We consider the new divisor 48 and the new remainder 16, and apply the division lemma to get
48 = 16 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 432 and 64 is 16
Notice that 16 = HCF(48,16) = HCF(64,48) = HCF(432,64) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 743 > 16, we apply the division lemma to 743 and 16, to get
743 = 16 x 46 + 7
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 7 and 16, to get
16 = 7 x 2 + 2
Step 3: We consider the new divisor 7 and the new remainder 2, and apply the division lemma to get
7 = 2 x 3 + 1
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 16 and 743 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(743,16) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 531 > 1, we apply the division lemma to 531 and 1, to get
531 = 1 x 531 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 531 is 1
Notice that 1 = HCF(531,1) .
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 432, 64, 743, 531?
Answer: HCF of 432, 64, 743, 531 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 64, 743, 531 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 64, 743, 531 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.