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 419, 6980, 7406 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 419, 6980, 7406 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 419, 6980, 7406 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 419, 6980, 7406 is 1.
HCF(419, 6980, 7406) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 419, 6980, 7406 is 1.
Step 1: Since 6980 > 419, we apply the division lemma to 6980 and 419, to get
6980 = 419 x 16 + 276
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 276 and 419, to get
419 = 276 x 1 + 143
Step 3: We consider the new divisor 276 and the new remainder 143, and apply the division lemma to get
276 = 143 x 1 + 133
We consider the new divisor 143 and the new remainder 133,and apply the division lemma to get
143 = 133 x 1 + 10
We consider the new divisor 133 and the new remainder 10,and apply the division lemma to get
133 = 10 x 13 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 419 and 6980 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(133,10) = HCF(143,133) = HCF(276,143) = HCF(419,276) = HCF(6980,419) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 7406 > 1, we apply the division lemma to 7406 and 1, to get
7406 = 1 x 7406 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 7406 is 1
Notice that 1 = HCF(7406,1) .
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 419, 6980, 7406?
Answer: HCF of 419, 6980, 7406 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 419, 6980, 7406 using Euclid's Algorithm?
Answer: For arbitrary numbers 419, 6980, 7406 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.