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 653, 295, 113 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 653, 295, 113 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 653, 295, 113 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 653, 295, 113 is 1.
HCF(653, 295, 113) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 653, 295, 113 is 1.
Step 1: Since 653 > 295, we apply the division lemma to 653 and 295, to get
653 = 295 x 2 + 63
Step 2: Since the reminder 295 ≠ 0, we apply division lemma to 63 and 295, to get
295 = 63 x 4 + 43
Step 3: We consider the new divisor 63 and the new remainder 43, and apply the division lemma to get
63 = 43 x 1 + 20
We consider the new divisor 43 and the new remainder 20,and apply the division lemma to get
43 = 20 x 2 + 3
We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get
20 = 3 x 6 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 653 and 295 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(43,20) = HCF(63,43) = HCF(295,63) = HCF(653,295) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 113 > 1, we apply the division lemma to 113 and 1, to get
113 = 1 x 113 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 113 is 1
Notice that 1 = HCF(113,1) .
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 653, 295, 113?
Answer: HCF of 653, 295, 113 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 653, 295, 113 using Euclid's Algorithm?
Answer: For arbitrary numbers 653, 295, 113 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.