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 564, 723, 400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 723, 400 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 564, 723, 400 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 564, 723, 400 is 1.
HCF(564, 723, 400) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 564, 723, 400 is 1.
Step 1: Since 723 > 564, we apply the division lemma to 723 and 564, to get
723 = 564 x 1 + 159
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 159 and 564, to get
564 = 159 x 3 + 87
Step 3: We consider the new divisor 159 and the new remainder 87, and apply the division lemma to get
159 = 87 x 1 + 72
We consider the new divisor 87 and the new remainder 72,and apply the division lemma to get
87 = 72 x 1 + 15
We consider the new divisor 72 and the new remainder 15,and apply the division lemma to get
72 = 15 x 4 + 12
We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get
15 = 12 x 1 + 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 564 and 723 is 3
Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(72,15) = HCF(87,72) = HCF(159,87) = HCF(564,159) = HCF(723,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 400 > 3, we apply the division lemma to 400 and 3, to get
400 = 3 x 133 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 400 is 1
Notice that 1 = HCF(3,1) = HCF(400,3) .
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 564, 723, 400?
Answer: HCF of 564, 723, 400 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 723, 400 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 723, 400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.