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 974, 8578, 4141 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 8578, 4141 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 974, 8578, 4141 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 974, 8578, 4141 is 1.
HCF(974, 8578, 4141) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 8578, 4141 is 1.
Step 1: Since 8578 > 974, we apply the division lemma to 8578 and 974, to get
8578 = 974 x 8 + 786
Step 2: Since the reminder 974 ≠ 0, we apply division lemma to 786 and 974, to get
974 = 786 x 1 + 188
Step 3: We consider the new divisor 786 and the new remainder 188, and apply the division lemma to get
786 = 188 x 4 + 34
We consider the new divisor 188 and the new remainder 34,and apply the division lemma to get
188 = 34 x 5 + 18
We consider the new divisor 34 and the new remainder 18,and apply the division lemma to get
34 = 18 x 1 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 8578 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(34,18) = HCF(188,34) = HCF(786,188) = HCF(974,786) = HCF(8578,974) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4141 > 2, we apply the division lemma to 4141 and 2, to get
4141 = 2 x 2070 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 4141 is 1
Notice that 1 = HCF(2,1) = HCF(4141,2) .
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 974, 8578, 4141?
Answer: HCF of 974, 8578, 4141 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 8578, 4141 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 8578, 4141 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.