Highest Common Factor of 560, 52416 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 560, 52416 i.e. 112 the largest integer that leaves a remainder zero for all numbers.
HCF of 560, 52416 is 112 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 560, 52416 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 560, 52416 is 112.
HCF(560, 52416) = 112
HCF of 560, 52416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 560, 52416 is 112.
Highest Common Factor of 560,52416 is 112
Step 1: Since 52416 > 560, we apply the division lemma to 52416 and 560, to get
52416 = 560 x 93 + 336
Step 2: Since the reminder 560 ≠ 0, we apply division lemma to 336 and 560, to get
560 = 336 x 1 + 224
Step 3: We consider the new divisor 336 and the new remainder 224, and apply the division lemma to get
336 = 224 x 1 + 112
We consider the new divisor 224 and the new remainder 112, and apply the division lemma to get
224 = 112 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 112, the HCF of 560 and 52416 is 112
Notice that 112 = HCF(224,112) = HCF(336,224) = HCF(560,336) = HCF(52416,560) .
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Frequently Asked Questions on HCF of 560, 52416 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 560, 52416?
Answer: HCF of 560, 52416 is 112 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 560, 52416 using Euclid's Algorithm?
Answer: For arbitrary numbers 560, 52416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.