Highest Common Factor of 280, 49 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 280, 49 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 280, 49 is 7 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 280, 49 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 280, 49 is 7.
HCF(280, 49) = 7
HCF of 280, 49 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 280, 49 is 7.
Highest Common Factor of 280,49 is 7
Step 1: Since 280 > 49, we apply the division lemma to 280 and 49, to get
280 = 49 x 5 + 35
Step 2: Since the reminder 49 ≠ 0, we apply division lemma to 35 and 49, to get
49 = 35 x 1 + 14
Step 3: We consider the new divisor 35 and the new remainder 14, and apply the division lemma to get
35 = 14 x 2 + 7
We consider the new divisor 14 and the new remainder 7, and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 280 and 49 is 7
Notice that 7 = HCF(14,7) = HCF(35,14) = HCF(49,35) = HCF(280,49) .
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Frequently Asked Questions on HCF of 280, 49 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 280, 49?
Answer: HCF of 280, 49 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 280, 49 using Euclid's Algorithm?
Answer: For arbitrary numbers 280, 49 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.