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, 7269 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 7269 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, 7269 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, 7269 is 1.
HCF(974, 7269) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 7269 is 1.
Step 1: Since 7269 > 974, we apply the division lemma to 7269 and 974, to get
7269 = 974 x 7 + 451
Step 2: Since the reminder 974 ≠ 0, we apply division lemma to 451 and 974, to get
974 = 451 x 2 + 72
Step 3: We consider the new divisor 451 and the new remainder 72, and apply the division lemma to get
451 = 72 x 6 + 19
We consider the new divisor 72 and the new remainder 19,and apply the division lemma to get
72 = 19 x 3 + 15
We consider the new divisor 19 and the new remainder 15,and apply the division lemma to get
19 = 15 x 1 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 974 and 7269 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(19,15) = HCF(72,19) = HCF(451,72) = HCF(974,451) = HCF(7269,974) .
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, 7269?
Answer: HCF of 974, 7269 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 7269 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 7269 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.