Highest Common Factor of 675, 603, 456, 472 using Euclid's algorithm
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 675, 603, 456, 472 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 603, 456, 472 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 675, 603, 456, 472 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 675, 603, 456, 472 is 1.
HCF(675, 603, 456, 472) = 1
HCF of 675, 603, 456, 472 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 603, 456, 472 is 1.
Highest Common Factor of 675,603,456,472 is 1
Step 1: Since 675 > 603, we apply the division lemma to 675 and 603, to get
675 = 603 x 1 + 72
Step 2: Since the reminder 603 ≠ 0, we apply division lemma to 72 and 603, to get
603 = 72 x 8 + 27
Step 3: We consider the new divisor 72 and the new remainder 27, and apply the division lemma to get
72 = 27 x 2 + 18
We consider the new divisor 27 and the new remainder 18,and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 675 and 603 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(72,27) = HCF(603,72) = HCF(675,603) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 456 > 9, we apply the division lemma to 456 and 9, to get
456 = 9 x 50 + 6
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 6 and 9, to get
9 = 6 x 1 + 3
Step 3: We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 456 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(456,9) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 3, we apply the division lemma to 472 and 3, to get
472 = 3 x 157 + 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 472 is 1
Notice that 1 = HCF(3,1) = HCF(472,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 675, 603, 456, 472 using Euclid's Algorithm
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 675, 603, 456, 472?
Answer: HCF of 675, 603, 456, 472 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 603, 456, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 603, 456, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.