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 105, 608 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 608 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 105, 608 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 105, 608 is 1.
HCF(105, 608) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 608 is 1.
Step 1: Since 608 > 105, we apply the division lemma to 608 and 105, to get
608 = 105 x 5 + 83
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 83 and 105, to get
105 = 83 x 1 + 22
Step 3: We consider the new divisor 83 and the new remainder 22, and apply the division lemma to get
83 = 22 x 3 + 17
We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get
22 = 17 x 1 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 105 and 608 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(83,22) = HCF(105,83) = HCF(608,105) .
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 105, 608?
Answer: HCF of 105, 608 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 608 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.