Highest Common Factor of 285, 722 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 285, 722 i.e. 19 the largest integer that leaves a remainder zero for all numbers.
HCF of 285, 722 is 19 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 285, 722 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 285, 722 is 19.
HCF(285, 722) = 19
HCF of 285, 722 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 285, 722 is 19.
Highest Common Factor of 285,722 is 19
Step 1: Since 722 > 285, we apply the division lemma to 722 and 285, to get
722 = 285 x 2 + 152
Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 152 and 285, to get
285 = 152 x 1 + 133
Step 3: We consider the new divisor 152 and the new remainder 133, and apply the division lemma to get
152 = 133 x 1 + 19
We consider the new divisor 133 and the new remainder 19, and apply the division lemma to get
133 = 19 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 285 and 722 is 19
Notice that 19 = HCF(133,19) = HCF(152,133) = HCF(285,152) = HCF(722,285) .
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Frequently Asked Questions on HCF of 285, 722 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 285, 722?
Answer: HCF of 285, 722 is 19 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 285, 722 using Euclid's Algorithm?
Answer: For arbitrary numbers 285, 722 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.