Highest Common Factor of 1984, 6720 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 1984, 6720 i.e. 64 the largest integer that leaves a remainder zero for all numbers.
HCF of 1984, 6720 is 64 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 1984, 6720 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 1984, 6720 is 64.
HCF(1984, 6720) = 64
HCF of 1984, 6720 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1984, 6720 is 64.
Highest Common Factor of 1984,6720 is 64
Step 1: Since 6720 > 1984, we apply the division lemma to 6720 and 1984, to get
6720 = 1984 x 3 + 768
Step 2: Since the reminder 1984 ≠ 0, we apply division lemma to 768 and 1984, to get
1984 = 768 x 2 + 448
Step 3: We consider the new divisor 768 and the new remainder 448, and apply the division lemma to get
768 = 448 x 1 + 320
We consider the new divisor 448 and the new remainder 320,and apply the division lemma to get
448 = 320 x 1 + 128
We consider the new divisor 320 and the new remainder 128,and apply the division lemma to get
320 = 128 x 2 + 64
We consider the new divisor 128 and the new remainder 64,and apply the division lemma to get
128 = 64 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 64, the HCF of 1984 and 6720 is 64
Notice that 64 = HCF(128,64) = HCF(320,128) = HCF(448,320) = HCF(768,448) = HCF(1984,768) = HCF(6720,1984) .
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Frequently Asked Questions on HCF of 1984, 6720 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 1984, 6720?
Answer: HCF of 1984, 6720 is 64 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1984, 6720 using Euclid's Algorithm?
Answer: For arbitrary numbers 1984, 6720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.