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 7326, 8442, 70432 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7326, 8442, 70432 is 2 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 7326, 8442, 70432 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 7326, 8442, 70432 is 2.
HCF(7326, 8442, 70432) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7326, 8442, 70432 is 2.
Step 1: Since 8442 > 7326, we apply the division lemma to 8442 and 7326, to get
8442 = 7326 x 1 + 1116
Step 2: Since the reminder 7326 ≠ 0, we apply division lemma to 1116 and 7326, to get
7326 = 1116 x 6 + 630
Step 3: We consider the new divisor 1116 and the new remainder 630, and apply the division lemma to get
1116 = 630 x 1 + 486
We consider the new divisor 630 and the new remainder 486,and apply the division lemma to get
630 = 486 x 1 + 144
We consider the new divisor 486 and the new remainder 144,and apply the division lemma to get
486 = 144 x 3 + 54
We consider the new divisor 144 and the new remainder 54,and apply the division lemma to get
144 = 54 x 2 + 36
We consider the new divisor 54 and the new remainder 36,and apply the division lemma to get
54 = 36 x 1 + 18
We consider the new divisor 36 and the new remainder 18,and apply the division lemma to get
36 = 18 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 7326 and 8442 is 18
Notice that 18 = HCF(36,18) = HCF(54,36) = HCF(144,54) = HCF(486,144) = HCF(630,486) = HCF(1116,630) = HCF(7326,1116) = HCF(8442,7326) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 70432 > 18, we apply the division lemma to 70432 and 18, to get
70432 = 18 x 3912 + 16
Step 2: Since the reminder 18 ≠ 0, we apply division lemma to 16 and 18, to get
18 = 16 x 1 + 2
Step 3: We consider the new divisor 16 and the new remainder 2, and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 18 and 70432 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(70432,18) .
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 7326, 8442, 70432?
Answer: HCF of 7326, 8442, 70432 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7326, 8442, 70432 using Euclid's Algorithm?
Answer: For arbitrary numbers 7326, 8442, 70432 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.