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, 663 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 974, 663 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, 663 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, 663 is 1.
HCF(974, 663) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 974, 663 is 1.
Step 1: Since 974 > 663, we apply the division lemma to 974 and 663, to get
974 = 663 x 1 + 311
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 311 and 663, to get
663 = 311 x 2 + 41
Step 3: We consider the new divisor 311 and the new remainder 41, and apply the division lemma to get
311 = 41 x 7 + 24
We consider the new divisor 41 and the new remainder 24,and apply the division lemma to get
41 = 24 x 1 + 17
We consider the new divisor 24 and the new remainder 17,and apply the division lemma to get
24 = 17 x 1 + 7
We consider the new divisor 17 and the new remainder 7,and apply the division lemma to get
17 = 7 x 2 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 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 663 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(17,7) = HCF(24,17) = HCF(41,24) = HCF(311,41) = HCF(663,311) = HCF(974,663) .
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, 663?
Answer: HCF of 974, 663 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 974, 663 using Euclid's Algorithm?
Answer: For arbitrary numbers 974, 663 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.