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 7784, 1588, 83969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7784, 1588, 83969 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 7784, 1588, 83969 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 7784, 1588, 83969 is 1.
HCF(7784, 1588, 83969) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7784, 1588, 83969 is 1.
Step 1: Since 7784 > 1588, we apply the division lemma to 7784 and 1588, to get
7784 = 1588 x 4 + 1432
Step 2: Since the reminder 1588 ≠ 0, we apply division lemma to 1432 and 1588, to get
1588 = 1432 x 1 + 156
Step 3: We consider the new divisor 1432 and the new remainder 156, and apply the division lemma to get
1432 = 156 x 9 + 28
We consider the new divisor 156 and the new remainder 28,and apply the division lemma to get
156 = 28 x 5 + 16
We consider the new divisor 28 and the new remainder 16,and apply the division lemma to get
28 = 16 x 1 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 7784 and 1588 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(28,16) = HCF(156,28) = HCF(1432,156) = HCF(1588,1432) = HCF(7784,1588) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 83969 > 4, we apply the division lemma to 83969 and 4, to get
83969 = 4 x 20992 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 83969 is 1
Notice that 1 = HCF(4,1) = HCF(83969,4) .
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 7784, 1588, 83969?
Answer: HCF of 7784, 1588, 83969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7784, 1588, 83969 using Euclid's Algorithm?
Answer: For arbitrary numbers 7784, 1588, 83969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.