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 983, 7426, 8800 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 983, 7426, 8800 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 983, 7426, 8800 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 983, 7426, 8800 is 1.
HCF(983, 7426, 8800) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 983, 7426, 8800 is 1.
Step 1: Since 7426 > 983, we apply the division lemma to 7426 and 983, to get
7426 = 983 x 7 + 545
Step 2: Since the reminder 983 ≠ 0, we apply division lemma to 545 and 983, to get
983 = 545 x 1 + 438
Step 3: We consider the new divisor 545 and the new remainder 438, and apply the division lemma to get
545 = 438 x 1 + 107
We consider the new divisor 438 and the new remainder 107,and apply the division lemma to get
438 = 107 x 4 + 10
We consider the new divisor 107 and the new remainder 10,and apply the division lemma to get
107 = 10 x 10 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 983 and 7426 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(107,10) = HCF(438,107) = HCF(545,438) = HCF(983,545) = HCF(7426,983) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8800 > 1, we apply the division lemma to 8800 and 1, to get
8800 = 1 x 8800 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 8800 is 1
Notice that 1 = HCF(8800,1) .
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 983, 7426, 8800?
Answer: HCF of 983, 7426, 8800 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 983, 7426, 8800 using Euclid's Algorithm?
Answer: For arbitrary numbers 983, 7426, 8800 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.