Highest Common Factor of 984, 828 using Euclid's algorithm
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 984, 828 i.e. 12 the largest integer that leaves a remainder zero for all numbers.
HCF of 984, 828 is 12 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 984, 828 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 984, 828 is 12.
HCF(984, 828) = 12
HCF of 984, 828 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 984, 828 is 12.
Highest Common Factor of 984,828 is 12
Step 1: Since 984 > 828, we apply the division lemma to 984 and 828, to get
984 = 828 x 1 + 156
Step 2: Since the reminder 828 ≠ 0, we apply division lemma to 156 and 828, to get
828 = 156 x 5 + 48
Step 3: We consider the new divisor 156 and the new remainder 48, and apply the division lemma to get
156 = 48 x 3 + 12
We consider the new divisor 48 and the new remainder 12, and apply the division lemma to get
48 = 12 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 984 and 828 is 12
Notice that 12 = HCF(48,12) = HCF(156,48) = HCF(828,156) = HCF(984,828) .
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Frequently Asked Questions on HCF of 984, 828 using Euclid's Algorithm
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 984, 828?
Answer: HCF of 984, 828 is 12 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 984, 828 using Euclid's Algorithm?
Answer: For arbitrary numbers 984, 828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.