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 608, 13128 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 13128 is 8 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 608, 13128 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 608, 13128 is 8.
HCF(608, 13128) = 8
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 13128 is 8.
Step 1: Since 13128 > 608, we apply the division lemma to 13128 and 608, to get
13128 = 608 x 21 + 360
Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 360 and 608, to get
608 = 360 x 1 + 248
Step 3: We consider the new divisor 360 and the new remainder 248, and apply the division lemma to get
360 = 248 x 1 + 112
We consider the new divisor 248 and the new remainder 112,and apply the division lemma to get
248 = 112 x 2 + 24
We consider the new divisor 112 and the new remainder 24,and apply the division lemma to get
112 = 24 x 4 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 608 and 13128 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(112,24) = HCF(248,112) = HCF(360,248) = HCF(608,360) = HCF(13128,608) .
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 608, 13128?
Answer: HCF of 608, 13128 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 13128 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 13128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.