Highest Common Factor of 3008, 1564 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 3008, 1564 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 3008, 1564 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 3008, 1564 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 3008, 1564 is 4.
HCF(3008, 1564) = 4
HCF of 3008, 1564 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3008, 1564 is 4.
Highest Common Factor of 3008,1564 is 4
Step 1: Since 3008 > 1564, we apply the division lemma to 3008 and 1564, to get
3008 = 1564 x 1 + 1444
Step 2: Since the reminder 1564 ≠ 0, we apply division lemma to 1444 and 1564, to get
1564 = 1444 x 1 + 120
Step 3: We consider the new divisor 1444 and the new remainder 120, and apply the division lemma to get
1444 = 120 x 12 + 4
We consider the new divisor 120 and the new remainder 4, and apply the division lemma to get
120 = 4 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3008 and 1564 is 4
Notice that 4 = HCF(120,4) = HCF(1444,120) = HCF(1564,1444) = HCF(3008,1564) .
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Frequently Asked Questions on HCF of 3008, 1564 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 3008, 1564?
Answer: HCF of 3008, 1564 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3008, 1564 using Euclid's Algorithm?
Answer: For arbitrary numbers 3008, 1564 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.