Highest Common Factor of 448, 1974 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 448, 1974 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 448, 1974 is 14 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 448, 1974 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 448, 1974 is 14.
HCF(448, 1974) = 14
HCF of 448, 1974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 448, 1974 is 14.
Highest Common Factor of 448,1974 is 14
Step 1: Since 1974 > 448, we apply the division lemma to 1974 and 448, to get
1974 = 448 x 4 + 182
Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 182 and 448, to get
448 = 182 x 2 + 84
Step 3: We consider the new divisor 182 and the new remainder 84, and apply the division lemma to get
182 = 84 x 2 + 14
We consider the new divisor 84 and the new remainder 14, and apply the division lemma to get
84 = 14 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 448 and 1974 is 14
Notice that 14 = HCF(84,14) = HCF(182,84) = HCF(448,182) = HCF(1974,448) .
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Frequently Asked Questions on HCF of 448, 1974 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 448, 1974?
Answer: HCF of 448, 1974 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 448, 1974 using Euclid's Algorithm?
Answer: For arbitrary numbers 448, 1974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.