Highest Common Factor of 2208, 1720 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 2208, 1720 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 2208, 1720 is 8 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 2208, 1720 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 2208, 1720 is 8.
HCF(2208, 1720) = 8
HCF of 2208, 1720 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2208, 1720 is 8.
Highest Common Factor of 2208,1720 is 8
Step 1: Since 2208 > 1720, we apply the division lemma to 2208 and 1720, to get
2208 = 1720 x 1 + 488
Step 2: Since the reminder 1720 ≠ 0, we apply division lemma to 488 and 1720, to get
1720 = 488 x 3 + 256
Step 3: We consider the new divisor 488 and the new remainder 256, and apply the division lemma to get
488 = 256 x 1 + 232
We consider the new divisor 256 and the new remainder 232,and apply the division lemma to get
256 = 232 x 1 + 24
We consider the new divisor 232 and the new remainder 24,and apply the division lemma to get
232 = 24 x 9 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 2208 and 1720 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(232,24) = HCF(256,232) = HCF(488,256) = HCF(1720,488) = HCF(2208,1720) .
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Frequently Asked Questions on HCF of 2208, 1720 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 2208, 1720?
Answer: HCF of 2208, 1720 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2208, 1720 using Euclid's Algorithm?
Answer: For arbitrary numbers 2208, 1720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.