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 674, 984 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 674, 984 is 2 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 674, 984 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 674, 984 is 2.
HCF(674, 984) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 674, 984 is 2.
Step 1: Since 984 > 674, we apply the division lemma to 984 and 674, to get
984 = 674 x 1 + 310
Step 2: Since the reminder 674 ≠ 0, we apply division lemma to 310 and 674, to get
674 = 310 x 2 + 54
Step 3: We consider the new divisor 310 and the new remainder 54, and apply the division lemma to get
310 = 54 x 5 + 40
We consider the new divisor 54 and the new remainder 40,and apply the division lemma to get
54 = 40 x 1 + 14
We consider the new divisor 40 and the new remainder 14,and apply the division lemma to get
40 = 14 x 2 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 674 and 984 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(40,14) = HCF(54,40) = HCF(310,54) = HCF(674,310) = HCF(984,674) .
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 674, 984?
Answer: HCF of 674, 984 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 674, 984 using Euclid's Algorithm?
Answer: For arbitrary numbers 674, 984 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.