Highest Common Factor of 722, 7785 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 722, 7785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 7785 is 1 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 722, 7785 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 722, 7785 is 1.
HCF(722, 7785) = 1
HCF of 722, 7785 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 7785 is 1.
Highest Common Factor of 722,7785 is 1
Step 1: Since 7785 > 722, we apply the division lemma to 7785 and 722, to get
7785 = 722 x 10 + 565
Step 2: Since the reminder 722 ≠ 0, we apply division lemma to 565 and 722, to get
722 = 565 x 1 + 157
Step 3: We consider the new divisor 565 and the new remainder 157, and apply the division lemma to get
565 = 157 x 3 + 94
We consider the new divisor 157 and the new remainder 94,and apply the division lemma to get
157 = 94 x 1 + 63
We consider the new divisor 94 and the new remainder 63,and apply the division lemma to get
94 = 63 x 1 + 31
We consider the new divisor 63 and the new remainder 31,and apply the division lemma to get
63 = 31 x 2 + 1
We consider the new divisor 31 and the new remainder 1,and apply the division lemma to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 722 and 7785 is 1
Notice that 1 = HCF(31,1) = HCF(63,31) = HCF(94,63) = HCF(157,94) = HCF(565,157) = HCF(722,565) = HCF(7785,722) .
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Frequently Asked Questions on HCF of 722, 7785 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 722, 7785?
Answer: HCF of 722, 7785 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 7785 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 7785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
