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 909, 513, 673, 748 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 513, 673, 748 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 909, 513, 673, 748 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 909, 513, 673, 748 is 1.
HCF(909, 513, 673, 748) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 909, 513, 673, 748 is 1.
Step 1: Since 909 > 513, we apply the division lemma to 909 and 513, to get
909 = 513 x 1 + 396
Step 2: Since the reminder 513 ≠ 0, we apply division lemma to 396 and 513, to get
513 = 396 x 1 + 117
Step 3: We consider the new divisor 396 and the new remainder 117, and apply the division lemma to get
396 = 117 x 3 + 45
We consider the new divisor 117 and the new remainder 45,and apply the division lemma to get
117 = 45 x 2 + 27
We consider the new divisor 45 and the new remainder 27,and apply the division lemma to get
45 = 27 x 1 + 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 909 and 513 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(45,27) = HCF(117,45) = HCF(396,117) = HCF(513,396) = HCF(909,513) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 673 > 9, we apply the division lemma to 673 and 9, to get
673 = 9 x 74 + 7
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 7 and 9, to get
9 = 7 x 1 + 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 9 and 673 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(673,9) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 748 > 1, we apply the division lemma to 748 and 1, to get
748 = 1 x 748 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 748 is 1
Notice that 1 = HCF(748,1) .
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 909, 513, 673, 748?
Answer: HCF of 909, 513, 673, 748 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 513, 673, 748 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 513, 673, 748 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.