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 499, 974, 130 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 499, 974, 130 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 499, 974, 130 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 499, 974, 130 is 1.
HCF(499, 974, 130) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 499, 974, 130 is 1.
Step 1: Since 974 > 499, we apply the division lemma to 974 and 499, to get
974 = 499 x 1 + 475
Step 2: Since the reminder 499 ≠ 0, we apply division lemma to 475 and 499, to get
499 = 475 x 1 + 24
Step 3: We consider the new divisor 475 and the new remainder 24, and apply the division lemma to get
475 = 24 x 19 + 19
We consider the new divisor 24 and the new remainder 19,and apply the division lemma to get
24 = 19 x 1 + 5
We consider the new divisor 19 and the new remainder 5,and apply the division lemma to get
19 = 5 x 3 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 499 and 974 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(475,24) = HCF(499,475) = HCF(974,499) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 130 > 1, we apply the division lemma to 130 and 1, to get
130 = 1 x 130 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 130 is 1
Notice that 1 = HCF(130,1) .
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 499, 974, 130?
Answer: HCF of 499, 974, 130 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 499, 974, 130 using Euclid's Algorithm?
Answer: For arbitrary numbers 499, 974, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.