Highest Common Factor of 980, 21324 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 980, 21324 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 980, 21324 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 980, 21324 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 980, 21324 is 4.
HCF(980, 21324) = 4
HCF of 980, 21324 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 980, 21324 is 4.
Highest Common Factor of 980,21324 is 4
Step 1: Since 21324 > 980, we apply the division lemma to 21324 and 980, to get
21324 = 980 x 21 + 744
Step 2: Since the reminder 980 ≠ 0, we apply division lemma to 744 and 980, to get
980 = 744 x 1 + 236
Step 3: We consider the new divisor 744 and the new remainder 236, and apply the division lemma to get
744 = 236 x 3 + 36
We consider the new divisor 236 and the new remainder 36,and apply the division lemma to get
236 = 36 x 6 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 980 and 21324 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(236,36) = HCF(744,236) = HCF(980,744) = HCF(21324,980) .
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Frequently Asked Questions on HCF of 980, 21324 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 980, 21324?
Answer: HCF of 980, 21324 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 980, 21324 using Euclid's Algorithm?
Answer: For arbitrary numbers 980, 21324 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
