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 642, 980, 600 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 642, 980, 600 is 2 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 642, 980, 600 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 642, 980, 600 is 2.
HCF(642, 980, 600) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 642, 980, 600 is 2.
Step 1: Since 980 > 642, we apply the division lemma to 980 and 642, to get
980 = 642 x 1 + 338
Step 2: Since the reminder 642 ≠ 0, we apply division lemma to 338 and 642, to get
642 = 338 x 1 + 304
Step 3: We consider the new divisor 338 and the new remainder 304, and apply the division lemma to get
338 = 304 x 1 + 34
We consider the new divisor 304 and the new remainder 34,and apply the division lemma to get
304 = 34 x 8 + 32
We consider the new divisor 34 and the new remainder 32,and apply the division lemma to get
34 = 32 x 1 + 2
We consider the new divisor 32 and the new remainder 2,and apply the division lemma to get
32 = 2 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 642 and 980 is 2
Notice that 2 = HCF(32,2) = HCF(34,32) = HCF(304,34) = HCF(338,304) = HCF(642,338) = HCF(980,642) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 600 > 2, we apply the division lemma to 600 and 2, to get
600 = 2 x 300 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 600 is 2
Notice that 2 = HCF(600,2) .
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 642, 980, 600?
Answer: HCF of 642, 980, 600 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 642, 980, 600 using Euclid's Algorithm?
Answer: For arbitrary numbers 642, 980, 600 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.