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 988, 74512 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 74512 is 4 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 988, 74512 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 988, 74512 is 4.
HCF(988, 74512) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 988, 74512 is 4.
Step 1: Since 74512 > 988, we apply the division lemma to 74512 and 988, to get
74512 = 988 x 75 + 412
Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 412 and 988, to get
988 = 412 x 2 + 164
Step 3: We consider the new divisor 412 and the new remainder 164, and apply the division lemma to get
412 = 164 x 2 + 84
We consider the new divisor 164 and the new remainder 84,and apply the division lemma to get
164 = 84 x 1 + 80
We consider the new divisor 84 and the new remainder 80,and apply the division lemma to get
84 = 80 x 1 + 4
We consider the new divisor 80 and the new remainder 4,and apply the division lemma to get
80 = 4 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 988 and 74512 is 4
Notice that 4 = HCF(80,4) = HCF(84,80) = HCF(164,84) = HCF(412,164) = HCF(988,412) = HCF(74512,988) .
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 988, 74512?
Answer: HCF of 988, 74512 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 74512 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 74512 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.